a-conjecture-of-mine

diff --git a/.gitignore b/.gitignore
@@ -1,9 +1,11 @@
-.idea
-.vscode
-*.exe
-*.img
-*.IMG
-Executables
-Statistics
-Latex
-Q#
+.idea
+.vscode
+*.exe
+*.img
+*.IMG
+bin
+bin/
+build
+Statistics
+Latex
+Q#

diff --git a/C++/main.cpp b/C++/main.cpp
@@ -1,83 +1,83 @@
-#include <chrono>
-#include <iostream>
-#include <string>
-#include <thread>
-#include <map>
-#include <vector>
-#include <charconv>
-
-#define SUCCESS 0
-#define FAIL 1
-#define INVALID_INPUT 2
-
-std::map<unsigned int, unsigned int> sums_cache;
-
-inline unsigned int sum_digits(unsigned int n)
-{
-    unsigned int sum = 0;
-    while (n != 0)
-    {
-        sum += (n % 10);
-        n /= 10;
-    }
-
-    return sum;
-}
-
-void get_counterexpl_thread(unsigned int start, unsigned int max, unsigned int interval)
-{
-    for (auto a = start; a <= max; a += interval)
-        for (auto b = a; b <= max; b++)
-        {
-            auto diff = sums_cache[a + b] - (sums_cache[a] + sums_cache[b]);
-
-            if (diff % 9 != 0)
-                exit(FAIL);
-        }
-}
-
-bool read_first_arg(int argc, char *argv[], unsigned int *value)
-{
-    if (argc > 1)
-    {
-        std::string value_str = argv[1];
-
-        try
-        {
-            *value = std::stoul(value_str);
-            return true;
-        }
-        catch (...)
-        {
-            return false;
-        }
-    }
-    else return false;
-}
-
-int main(int argc, char *argv[])
-{
-    unsigned int max;
-    if (read_first_arg(argc, argv, &max))
-    {
-        auto n_threads = std::thread::hardware_concurrency();
-        std::vector<std::thread> threads;
-        
-        // Builds the sums cache
-        for (int i = 0; i != 2 * max; i++)
-            sums_cache[i] = sum_digits(i);
-
-        // Distributes calculations across threads evenlly
-        for (int i = 0; i < n_threads; i++)
-        {
-            auto thread = std::thread(get_counterexpl_thread, i, max, n_threads);
-            thread.join();
-        }
-
-        return SUCCESS;
-    }
-    else
-    {
-        return INVALID_INPUT;
-    }
+#include <chrono>
+#include <iostream>
+#include <string>
+#include <thread>
+#include <map>
+#include <vector>
+#include <charconv>
+
+#define SUCCESS 0
+#define FAIL 1
+#define INVALID_INPUT 2
+
+std::map<unsigned int, unsigned int> sums_cache;
+
+inline unsigned int sum_digits(unsigned int n)
+{
+    unsigned int sum = 0;
+    while (n != 0)
+    {
+        sum += (n % 10);
+        n /= 10;
+    }
+
+    return sum;
+}
+
+void get_counterexpl_thread(unsigned int start, unsigned int max, unsigned int interval)
+{
+    for (auto a = start; a <= max; a += interval)
+        for (auto b = a; b <= max; b++)
+        {
+            auto diff = sums_cache[a + b] - (sums_cache[a] + sums_cache[b]);
+
+            if (diff % 9 != 0)
+                exit(FAIL);
+        }
+}
+
+bool read_first_arg(int argc, char *argv[], unsigned int *value)
+{
+    if (argc > 1)
+    {
+        std::string value_str = argv[1];
+
+        try
+        {
+            *value = std::stoul(value_str);
+            return true;
+        }
+        catch (...)
+        {
+            return false;
+        }
+    }
+    else return false;
+}
+
+int main(int argc, char *argv[])
+{
+    unsigned int max;
+    if (read_first_arg(argc, argv, &max))
+    {
+        auto n_threads = std::thread::hardware_concurrency();
+        std::vector<std::thread> threads;
+        
+        // Builds the sums cache
+        for (int i = 0; i != 2 * max; i++)
+            sums_cache[i] = sum_digits(i);
+
+        // Distributes calculations across threads evenlly
+        for (int i = 0; i < n_threads; i++)
+        {
+            auto thread = std::thread(get_counterexpl_thread, i, max, n_threads);
+            thread.join();
+        }
+
+        return SUCCESS;
+    }
+    else
+    {
+        return INVALID_INPUT;
+    }
 } 
\ No newline at end of file

diff --git a/C/main.c b/C/main.c
@@ -1,141 +1,141 @@
-#include <stdlib.h>
-#include <stdio.h>
-#include <pthread.h>
-
-// Imports to get system information
-#ifdef _WIN32
-#include <windows.h>
-#elif MACOS
-#include <sys/param.h>
-#include <sys/sysctl.h>
-#else
-#include <unistd.h>
-#endif
-
-#define SUCCESS 0
-#define FAIL 1
-#define INVALID_INPUT 2
-
-// This program is a simple test for the following conjecture:
-
-// Let S: N -> N be the sum of the digits of a positive integer.
-// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
-
-int err = SUCCESS; // Global error condition
-int *sums_cache;   // Shared memory between threads
-
-// Memory structure to pass arguments to threads using the pthreads library
-struct iter_info
-{
-    int start;
-    int interval;
-    int max;
-};
-
-// Find the number of processors on host machine
-int get_num_cores()
-{
-#ifdef WIN32
-    SYSTEM_INFO sysinfo;
-    GetSystemInfo(&sysinfo);
-    return sysinfo.dwNumberOfProcessors;
-#elif MACOS
-    int nm[2];
-    size_t len = 4;
-    uint32_t count;
-
-    nm[0] = CTL_HW;
-    nm[1] = HW_AVAILCPU;
-    sysctl(nm, 2, &count, &len, NULL, 0);
-
-    if (count < 1)
-    {
-        nm[1] = HW_NCPU;
-        sysctl(nm, 2, &count, &len, NULL, 0);
-        if (count < 1)
-        {
-            count = 1;
-        }
-    }
-    return count;
-#else
-    return sysconf(_SC_NPROCESSORS_ONLN);
-#endif
-}
-
-int sum_digits(unsigned n)
-{
-    int parc = n;
-    int sum = 0;
-
-    while (parc > 0)
-    {
-        sum += parc % 10;
-        parc /= 10;
-    }
-    return sum;
-}
-
-int get_counterexpl_iter(struct iter_info *iter)
-{
-    for (int a = iter->start; a <= iter->max; a += iter->interval)
-        for (int b = a; b <= iter->max; b++)
-        {
-            if ((sums_cache[a + b] - (sums_cache[a] + sums_cache[b])) % 9 != 0)
-            {
-                err = 1;
-                return FAIL;
-            }
-        }
-
-    return SUCCESS;
-}
-
-int main(int argc, char *argv[])
-{
-    if (argc > 1) {
-
-        // Get the length of argv[1]
-        int len;
-        for (len = 0; argv[len] != '\0'; len++);
-
-        // Check if argv[1] is numeric
-        for (int i = 0; i < len; i++)
-            if (argv[1][i] < '0' || argv[1][i] > '9')
-                return INVALID_INPUT;
-
-        unsigned int max = strtoul(argv[1], NULL, 10);
-        int n_threads = get_num_cores();
-        pthread_t thread_ids[n_threads];
-        struct iter_info thread_iters[n_threads];
-
-        // Create the sums cache
-        int sums_c = 2 * max;
-        sums_cache = malloc(sizeof(int) * sums_c * 2); //original (sizeof(int)* sums_c) causing seg faults in multi-threading
-        for (int i = 0; i <= sums_c; i++)
-            sums_cache[i] = sum_digits(i);
-
-
-        // Create the threads, divide the task into number of threads equivalent to number
-        // of cores on the host machine
-        for (int i = 0; i < n_threads; i++)
-        {
-            thread_iters[i].start = i;
-            thread_iters[i].max = max;
-            thread_iters[i].interval = n_threads;
-            err = pthread_create(&thread_ids[i], NULL, get_counterexpl_iter, &thread_iters[i]);
-
-            if (err) printf("Unable to create thread : %d\n", err);
-        }
-
-        for (int i = 0; i < n_threads; i++)
-        {
-            err = pthread_join(thread_ids[i], NULL);
-            if (err) printf("Unable to join threads : %d\n", err);
-        }
-
-        return err;
-    } else {
-        return INVALID_INPUT;
-    }
-}
+#include <stdlib.h>
+#include <stdio.h>
+#include <pthread.h>
+
+// Imports to get system information
+#ifdef _WIN32
+#include <windows.h>
+#elif MACOS
+#include <sys/param.h>
+#include <sys/sysctl.h>
+#else
+#include <unistd.h>
+#endif
+
+#define SUCCESS 0
+#define FAIL 1
+#define INVALID_INPUT 2
+
+// This program is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
+
+int err = SUCCESS; // Global error condition
+int *sums_cache;   // Shared memory between threads
+
+// Memory structure to pass arguments to threads using the pthreads library
+struct iter_info
+{
+    int start;
+    int interval;
+    int max;
+};
+
+// Find the number of processors on host machine
+int get_num_cores()
+{
+#ifdef WIN32
+    SYSTEM_INFO sysinfo;
+    GetSystemInfo(&sysinfo);
+    return sysinfo.dwNumberOfProcessors;
+#elif MACOS
+    int nm[2];
+    size_t len = 4;
+    uint32_t count;
+
+    nm[0] = CTL_HW;
+    nm[1] = HW_AVAILCPU;
+    sysctl(nm, 2, &count, &len, NULL, 0);
+
+    if (count < 1)
+    {
+        nm[1] = HW_NCPU;
+        sysctl(nm, 2, &count, &len, NULL, 0);
+        if (count < 1)
+        {
+            count = 1;
+        }
+    }
+    return count;
+#else
+    return sysconf(_SC_NPROCESSORS_ONLN);
+#endif
+}
+
+int sum_digits(unsigned n)
+{
+    int parc = n;
+    int sum = 0;
+
+    while (parc > 0)
+    {
+        sum += parc % 10;
+        parc /= 10;
+    }
+    return sum;
+}
+
+int get_counterexpl_iter(struct iter_info *iter)
+{
+    for (int a = iter->start; a <= iter->max; a += iter->interval)
+        for (int b = a; b <= iter->max; b++)
+        {
+            if ((sums_cache[a + b] - (sums_cache[a] + sums_cache[b])) % 9 != 0)
+            {
+                err = 1;
+                return FAIL;
+            }
+        }
+
+    return SUCCESS;
+}
+
+int main(int argc, char *argv[])
+{
+    if (argc > 1)
+    {
+        // Check if argv[1] is numeric
+        int i = 0;
+        while (argv[1][i] != '\0')
+        {
+            if (argv[1][i] < '0' || argv[1][i] > '9')
+                return INVALID_INPUT;
+
+            i++;
+        }
+
+        unsigned int max = strtoul(argv[1], NULL, 10);
+        int n_threads = get_num_cores();
+        pthread_t thread_ids[n_threads];
+        struct iter_info thread_iters[n_threads];
+
+        // Create the sums cache
+        int sums_c = 2 * max;
+        sums_cache = malloc(sizeof(int) * sums_c * 2); //original (sizeof(int)* sums_c) causing seg faults in multi-threading
+        for (int i = 0; i <= sums_c; i++)
+            sums_cache[i] = sum_digits(i);
+
+
+        // Create the threads, divide the task into number of threads equivalent to number
+        // of cores on the host machine
+        for (int i = 0; i < n_threads; i++)
+        {
+            thread_iters[i].start = i;
+            thread_iters[i].max = max;
+            thread_iters[i].interval = n_threads;
+            err = pthread_create(&thread_ids[i], NULL, get_counterexpl_iter, &thread_iters[i]);
+
+            if (err) fprintf(stderr, "Unable to create thread : %d\n", err);
+        }
+
+        for (int i = 0; i < n_threads; i++)
+        {
+            err = pthread_join(thread_ids[i], NULL);
+            if (err) fprintf(stderr, "Unable to join threads : %d\n", err);
+        }
+
+        return err;
+    }
+    else return INVALID_INPUT;
+}

diff --git a/Elixir/conjecture/.formatter.exs b/Elixir/conjecture/.formatter.exs
@@ -0,0 +1,4 @@
+# Used by "mix format"
+[
+  inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
+]

diff --git a/Elixir/conjecture/.gitignore b/Elixir/conjecture/.gitignore
@@ -0,0 +1,24 @@
+# The directory Mix will write compiled artifacts to.
+/_build/
+
+# If you run "mix test --cover", coverage assets end up here.
+/cover/
+
+# The directory Mix downloads your dependencies sources to.
+/deps/
+
+# Where third-party dependencies like ExDoc output generated docs.
+/doc/
+
+# Ignore .fetch files in case you like to edit your project deps locally.
+/.fetch
+
+# If the VM crashes, it generates a dump, let's ignore it too.
+erl_crash.dump
+
+# Also ignore archive artifacts (built via "mix archive.build").
+*.ez
+
+# Ignore package tarball (built via "mix hex.build").
+conjecture-*.tar
+

diff --git a/Elixir/conjecture/lib/conjecture.ex b/Elixir/conjecture/lib/conjecture.ex
@@ -0,0 +1,73 @@
+defmodule Conjecture do
+  INVALID_INPUT = 2
+
+  def main do 
+    case System.argv() |> Enum.map(fn s -> Integer.parse s end) do
+      [{max, ""}, {n_processes, ""}] -> run max, n_processes
+      _ -> System.halt INVALID_INPUT
+    end
+  end
+
+  def run max, n_processes do
+    if max < 0 or n_processes <= 0 do
+      System.halt INVALID_INPUT
+    else
+      # Spawn a new process for each starting index from 0 to ``max`
+      f = fn i -> spawn fn -> counterexpl i, max, n_processes end end
+      pids = Enum.map 0..max, f
+
+      # Send the current PID to each process
+      Enum.map pids, fn pid -> send pid, self() end
+      listen
+    end
+  end
+
+  # Listen for messages on all processes
+  def listen do
+    receive do
+      :found -> System.halt 1
+      :ok -> listen
+    end
+  end
+
+  def counterexpl start, max, n_processes do
+    receive do
+      parent_pid ->
+        if counterexpl_loop start, max, n_processes do
+          send parent_pid, :found
+        else
+          send parent_pid, :ok
+        end
+    end
+  end
+
+  def counterexpl_loop a, max, n_processes do
+    cond do
+      iter a, 0 -> true
+      a + n_processes <= max ->
+        counterexpl_loop (a + n_processes), max, n_processes
+      true -> false
+    end
+  end
+
+  def iter a, b do
+    cond do
+      test a, b -> true
+      b + 1 < a -> iter a, b + 1
+      true -> false
+    end
+  end
+
+  def test a, b do
+    rem (sum (a + b) - sum a - sum b), 9 == 0
+  end
+
+  def sum 0 do 0 end
+
+  def sum n do
+    d = rem n, 10
+    r = div n, 10
+
+    d + sum r
+  end
+end

diff --git a/Elixir/conjecture/mix.exs b/Elixir/conjecture/mix.exs
@@ -0,0 +1,28 @@
+defmodule Conjecture.MixProject do
+  use Mix.Project
+
+  def project do
+    [
+      app: :conjecture,
+      version: "0.1.0",
+      elixir: "~> 1.9",
+      start_permanent: Mix.env() == :prod,
+      deps: deps()
+    ]
+  end
+
+  # Run "mix help compile.app" to learn about applications.
+  def application do
+    [
+      extra_applications: [:logger]
+    ]
+  end
+
+  # Run "mix help deps" to learn about dependencies.
+  defp deps do
+    [
+      # {:dep_from_hexpm, "~> 0.3.0"},
+      # {:dep_from_git, git: "https://github.com/elixir-lang/my_dep.git", tag: "0.1.0"}
+    ]
+  end
+end

diff --git a/Elixir/conjecture/test/conjecture_test.exs b/Elixir/conjecture/test/conjecture_test.exs
@@ -0,0 +1,8 @@
+defmodule ConjectureTest do
+  use ExUnit.Case
+  doctest Conjecture
+
+  test "greets the world" do
+    assert Conjecture.hello() == :world
+  end
+end

diff --git a/Elixir/conjecture/test/test_helper.exs b/Elixir/conjecture/test/test_helper.exs
@@ -0,0 +1 @@
+ExUnit.start()

diff --git a/Go/conjecture.go b/Go/conjecture.go
@@ -1,120 +1,120 @@
-package main
-
-// This program is a simple test for the following conjecture:
-
-// Let S: N -> N be the sum of the digits of a positive integer.
-// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
-
-import (
-	"os"
-	"strconv"
-)
-
-type iter struct {
-	Start    uint
-	Max      uint
-	Interval uint
-}
-
-const success = 0
-const fail = 1
-const invalidInput = 2
-
-func main() {
-	if len(os.Args) > 0 {
-		nThreads := uint(1)
-
-		if len(os.Args) > 1 {
-			if arg, err := strconv.ParseUint(os.Args[2], 10, 64); err == nil && arg >= 1 {
-				nThreads = uint(arg)
-			}
-		}
-
-		if max, err := strconv.ParseUint(os.Args[0], 10, 64); err == nil {
-			if getCounterexample(uint(max), nThreads) {
-				os.Exit(fail)
-			} else {
-				os.Exit(success)
-			}
-		} else {
-			os.Exit(invalidInput)
-		}
-	} else {
-		os.Exit(invalidInput)
-	}
-
-}
-
-func getCounterexample(max uint, nThreads uint) bool {
-	sums := getSums(max)
-
-	if nThreads > 1 {
-		channels := make([](chan bool), nThreads)
-
-		// Compute the result of each sub-range
-		for i := 0; i < int(nThreads); i++ {
-			channels[i] = make(chan bool)
-			it := iter{uint(i), max, nThreads}
-
-			go getCounterIter(it, &sums, channels[i])
-		}
-
-		// Listen for the computation to finish
-		for _, c := range channels {
-			if msg := <-c; msg {
-				return true
-			}
-		}
-	} else {
-		c := make(chan bool)
-		it := iter{0, max, 1}
-
-		go getCounterIter(it, &sums, c)
-
-		return <-c
-	}
-
-	return false
-}
-
-func getCounterIter(it iter, sums *[]int, c chan bool) {
-	for a := it.Start; a <= it.Max; a += it.Interval {
-		for b := a; b <= it.Max; b++ {
-			diff := (*sums)[a+b] - (*sums)[a] - (*sums)[b]
-
-			if diff%9 != 0 {
-				c <- true
-				close(c)
-
-				return
-			}
-		}
-	}
-
-	c <- false
-	close(c)
-}
-
-func getSums(max uint) []int {
-	maxRange := 2*max + 1
-	sums := make([]int, maxRange)
-
-	for i := range sums {
-		sums[i] = sumDigits(uint(i))
-	}
-
-	return sums
-}
-
-func sumDigits(n uint) int {
-	var sum uint
-
-	for {
-		if n <= 0 {
-			return int(sum)
-		}
-
-		sum += n % 10
-		n /= 10
-	}
-}
+package main
+
+// This program is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+import (
+	"os"
+	"strconv"
+)
+
+type iter struct {
+	Start    uint
+	Max      uint
+	Interval uint
+}
+
+const success = 0
+const fail = 1
+const invalidInput = 2
+
+func main() {
+	if len(os.Args) > 0 {
+		nThreads := uint(1)
+
+		if len(os.Args) > 1 {
+			if arg, err := strconv.ParseUint(os.Args[2], 10, 64); err == nil && arg >= 1 {
+				nThreads = uint(arg)
+			}
+		}
+
+		if max, err := strconv.ParseUint(os.Args[0], 10, 64); err == nil {
+			if getCounterexample(uint(max), nThreads) {
+				os.Exit(fail)
+			} else {
+				os.Exit(success)
+			}
+		} else {
+			os.Exit(invalidInput)
+		}
+	} else {
+		os.Exit(invalidInput)
+	}
+
+}
+
+func getCounterexample(max uint, nThreads uint) bool {
+	sums := getSums(max)
+
+	if nThreads > 1 {
+		channels := make([](chan bool), nThreads)
+
+		// Compute the result of each sub-range
+		for i := 0; i < int(nThreads); i++ {
+			channels[i] = make(chan bool)
+			it := iter{uint(i), max, nThreads}
+
+			go getCounterIter(it, &sums, channels[i])
+		}
+
+		// Listen for the computation to finish
+		for _, c := range channels {
+			if msg := <-c; msg {
+				return true
+			}
+		}
+	} else {
+		c := make(chan bool)
+		it := iter{0, max, 1}
+
+		go getCounterIter(it, &sums, c)
+
+		return <-c
+	}
+
+	return false
+}
+
+func getCounterIter(it iter, sums *[]int, c chan bool) {
+	for a := it.Start; a <= it.Max; a += it.Interval {
+		for b := a; b <= it.Max; b++ {
+			diff := (*sums)[a+b] - (*sums)[a] - (*sums)[b]
+
+			if diff%9 != 0 {
+				c <- true
+				close(c)
+
+				return
+			}
+		}
+	}
+
+	c <- false
+	close(c)
+}
+
+func getSums(max uint) []int {
+	maxRange := 2*max + 1
+	sums := make([]int, maxRange)
+
+	for i := range sums {
+		sums[i] = sumDigits(uint(i))
+	}
+
+	return sums
+}
+
+func sumDigits(n uint) int {
+	var sum uint
+
+	for {
+		if n <= 0 {
+			return int(sum)
+		}
+
+		sum += n % 10
+		n /= 10
+	}
+}

diff --git a/Haskell/.gitignore b/Haskell/.gitignore
@@ -1,4 +0,0 @@
-.stack-work
-.idea
-*.cabal
-stack.yaml-
\ No newline at end of file

diff --git a/Haskell/Main.hs b/Haskell/Main.hs
@@ -0,0 +1,76 @@
+-- The following program is a simple test for the following conjecture:
+
+-- Let S: N -> N be the sum of the digits of a positive integer.
+-- For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
+
+module Main where
+
+import Numeric (readDec)
+import Numeric.Natural
+import System.Environment
+import System.Exit
+import Control.Monad (foldM)
+import Data.Map (Map, insert, empty)
+import qualified Data.Map
+
+main :: IO Int
+main = do
+    args <- getArgs
+        
+    case head' args >>= Just . readDec of
+        Just [(max, "")] ->
+            if counter' max then exitFailure else exitSuccess
+        _ -> exitInvalidInput
+    
+    where head' [] = Nothing
+          head' xs = Just (head xs)
+
+-- Calculates the sum of the digits of `n`.
+sum' :: Natural -> Int
+sum' n
+     | n < 10 = fromEnum n
+     | otherwise = fromEnum (n `mod` 10) + sum' (n `div` 10)
+
+-- Returns `Just updated` if the if the conjecture holds for pair, where
+-- `updated` is an updated versions of the sums cache provided by `sums`.
+-- Otherwise returns `Nothing`.
+test' :: Map Natural Int -> (Natural, Natural) -> Maybe (Map Natural Int)
+test' sums pair =
+    case diff sums pair of
+        Left updated ->
+            test' updated pair
+
+        Right dif ->
+            if dif `mod` 9 == 0 then Just sums else Nothing
+
+-- Given a cache of the image of `sum'`, attemps to lookup `sum' a`, `sum' b`
+-- and `sum' $ a + b`.
+-- If the lookup succeeds, returns `Right (sum' (a + b) - sum' a - sum' a)`.
+-- Otherwise inserts the value that caused the failure to `sums` and returns
+-- `Left sums`.
+diff :: Map Natural Int -> (Natural, Natural) -> Either (Map Natural Int) Int
+diff sums (a, b) = do
+    sa  <- lookupOrInsert a
+    sb  <- lookupOrInsert b
+    sab <- lookupOrInsert $ a + b
+
+    pure $ sab - sa - sb
+    where lookupOrInsert x =
+            case Data.Map.lookup x sums of
+                Just sx -> Right sx
+                
+                Nothing -> Left (insert x (sum' x) sums)
+
+-- Checks if there is any counterexample in
+-- [(a, b) | a <- [0..max], b <- [a..max]].
+--
+-- Returns `True` if a counter example was found.
+-- Otherwise returns `False`.
+counter' :: Natural -> Bool
+counter' max =
+    case foldM test' empty [(a, b) | a <- [0..max], b <- [a..max]] of
+        Nothing -> True
+        Just _  -> False
+
+exitInvalidInput :: IO Int
+exitInvalidInput = exitWith $ ExitFailure 2

diff --git a/Haskell/app/Main.hs b/Haskell/app/Main.hs
@@ -1,76 +0,0 @@
--- The following program is a simple test for the following conjecture:
-
--- Let S: N -> N be the sum of the digits of a positive integer.
--- For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
-
-module Main where
-
-import Numeric (readDec)
-import Numeric.Natural
-import System.Environment
-import System.Exit
-import Control.Monad (foldM)
-import Data.Map (Map, insert, empty)
-import qualified Data.Map
-
-main :: IO Int
-main = do
-    args <- getArgs
-        
-    case head' args >>= Just . readDec of
-        Just [(max, "")] ->
-            if counter' max then exitFailure else exitSuccess
-        _ -> exitInvalidInput
-    
-    where head' [] = Nothing
-          head' xs = Just (head xs)
-
--- Calculates the sum of the digits of `n`.
-sum' :: Natural -> Int
-sum' n
-    | n < 10 = fromEnum n
-    | otherwise = fromEnum (n `mod` 10) + sum' (n `div` 10)
-
--- Returns `Just updated` if the if the conjecture holds for pair, where
--- `updated` is an updated versions of the sums cache provided by `sums`.
--- Otherwise returns `Nothing`.
-test' :: Map Natural Int -> (Natural, Natural) -> Maybe (Map Natural Int)
-test' sums pair =
-    case diff sums pair of
-        Left updated ->
-            test' updated pair
-
-        Right dif ->
-            if dif `mod` 9 == 0 then Just sums else Nothing
-
--- Given a cache of the image of `sum'`, attemps to lookup `sum' a`, `sum' b`
--- and `sum' $ a + b`.
--- If the lookup succeeds, returns `Right (sum' (a + b) - sum' a - sum' a)`.
--- Otherwise inserts the value that caused the failure to `sums` and returns
--- `Left sums`.
-diff :: Map Natural Int -> (Natural, Natural) -> Either (Map Natural Int) Int
-diff sums (a, b) = do
-    sa  <- lookupOrInsert a
-    sb  <- lookupOrInsert b
-    sab <- lookupOrInsert $ a + b
-
-    pure $ sab - sa - sb
-    where lookupOrInsert x =
-            case Data.Map.lookup x sums of
-                Just sx -> Right sx
-                
-                Nothing -> Left (insert x (sum' x) sums)
-
--- Checks if there is any counterexample in
--- [(a, b) | a <- [0..max], b <- [a..max]].
---
--- Returns `True` if a counter example was found.
--- Otherwise returns `False`.
-counter' :: Natural -> Bool
-counter' max =
-    case foldM test' empty [(a, b) | a <- [0..max], b <- [a..max]] of
-        Nothing -> True
-        Just _  -> False
-
-exitInvalidInput :: IO Int
-exitInvalidInput = exitWith $ ExitFailure 2-
\ No newline at end of file

diff --git a/Haskell/package.yaml b/Haskell/package.yaml
@@ -1,33 +0,0 @@
-name:                conjecture
-version:             1.0.0.0
-license:             MIT
-author:              "GarkGarcia"
-maintainer:          "gark.garcia@protonmail.com"
-copyright:           "2019 GarkGarcia"
-
-extra-source-files: []
-
-# Metadata used when publishing your package
-# synopsis:            Short description of your package
-# category:            Web
-
-# To avoid duplicated efforts in documentation and dealing with the
-# complications of embedding Haddock markup inside cabal files, it is
-# common to point users to the README.md file.
-description: This program is a simple test for a little conjecture of mine.
-
-dependencies:
-  - base >= 4.7 && < 5
-  - containers == 0.6.2.1
-
-executables:
-  haskell:
-    main: Main.hs
-    source-dirs: app
-    ghc-options:
-      - -threaded
-      - -rtsopts
-      - -with-rtsopts=-N
-      - -O
-    dependencies:
-      - containers == 0.6.2.1-
\ No newline at end of file

diff --git a/Haskell/stack.yaml b/Haskell/stack.yaml
@@ -1,68 +0,0 @@
-# This file was automatically generated by 'stack init'
-#
-# Some commonly used options have been documented as comments in this file.
-# For advanced use and comprehensive documentation of the format, please see:
-# https://docs.haskellstack.org/en/stable/yaml_configuration/
-
-# Resolver to choose a 'specific' stackage snapshot or a compiler version.
-# A snapshot resolver dictates the compiler version and the set of packages
-# to be used for project dependencies. For example:
-#
-# resolver: lts-3.5
-# resolver: nightly-2015-09-21
-# resolver: ghc-7.10.2
-#
-# The location of a snapshot can be provided as a file or url. Stack assumes
-# a snapshot provided as a file might change, whereas a url resource does not.
-#
-# resolver: ./custom-snapshot.yaml
-# resolver: https://example.com/snapshots/2018-01-01.yaml
-resolver: lts-13.10
-
-# User packages to be built.
-# Various formats can be used as shown in the example below.
-#
-# packages:
-# - some-directory
-# - https://example.com/foo/bar/baz-0.0.2.tar.gz
-# - location:
-#    git: https://github.com/commercialhaskell/stack.git
-#    commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
-# - location: https://github.com/commercialhaskell/stack/commit/e7b331f14bcffb8367cd58fbfc8b40ec7642100a
-#  subdirs:
-#  - auto-update
-#  - wai
-packages:
-  - .
-# Dependency packages to be pulled from upstream that are not in the resolver
-# using the same syntax as the packages field.
-# (e.g., acme-missiles-0.3)
-extra-deps: []
-#  - conduit-1.2.13.1@sha256:afd4db7fe66ae7af3d418e1a932384a8dee08df2f6299cca80e53ba964ce1228
-#  - conduit-extra-1.1.17@sha256:a4e6f476ba86db2c7cb76993b43b2a156b010de2917d239af66f9d7e7599e269
-#  - resourcet-1.1.11@sha256:096a3db6774a728bbe264e3e25c4e40d60e527ebd4b90c0b311deaa8d4cf4f27
-#  - streaming-commons-0.1.19@sha256:3a02f84578f75eac1425dca877f8d697b68d379a21970c1dad96196620404803
-
-# Override default flag values for local packages and extra-deps
-# flags: {}
-
-# Extra package databases containing global packages
-# extra-package-dbs: []
-
-# Control whether we use the GHC we find on the path
-# system-ghc: true
-#
-# Require a specific version of stack, using version ranges
-# require-stack-version: -any # Default
-# require-stack-version: ">=1.9"
-#
-# Override the architecture used by stack, especially useful on Windows
-# arch: i386
-# arch: x86_64
-#
-# Extra directories used by stack for building
-# extra-include-dirs: [/path/to/dir]
-# extra-lib-dirs: [/path/to/dir]
-#
-# Allow a newer minor version of GHC than the snapshot specifies
-# compiler-check: newer-minor

diff --git a/Java/.gitignore b/Java/.gitignore
@@ -1,4 +1,4 @@
-.idea
-out
-src/META-INF
-Java.iml
+.idea
+out
+src/META-INF
+Java.iml

diff --git a/Java/src/conjecture/Main.java b/Java/src/conjecture/Main.java
@@ -1,64 +1,64 @@
-package conjecture;
-
-// The following program is a simple test for the following conjecture:
-
-// Let S: N -> N be the sum of the digits of a positive integer.
-// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
-
-import java.util.InputMismatchException;
-
-public class Main {
-    private static final int SUCCESS = 0;
-    private static final int FAIL = 1;
-    private static final int INVALID_INPUT = 2;
-
-    public static void main(String[] args) {
-        try {
-            int max = Integer.parseInt(args[0]);
-
-            if (getCounterexample(max)) {
-                System.exit(FAIL);
-            } else {
-                System.exit(SUCCESS);
-            }
-        } catch (InputMismatchException error) {
-            System.exit(INVALID_INPUT);
-        }
-
-    }
-
-    private static Boolean getCounterexample(int max) {
-        int[] sum = getSums(max);
-
-        for (int a = 0; a <= max; a++)
-            for (int b = a; b <= max; b++) {
-                int diff = sum[a + b] - (sum[a] + sum[b]);
-
-                if (diff % 9 != 0)
-                    return true;
-            }
-
-        return false;
-    }
-
-    private static int[] getSums(int max) {
-        int maxRange = 2 * (max + 1);
-        int[] sums = new int[maxRange];
-
-        for (int i = 0; i < maxRange; i++)
-            sums[i] = sumDigits(i);
-
-        return sums;
-    }
-
-    private static int sumDigits(int n) {
-        int num = Math.abs(n), sum = 0;
-
-        while (num > 0) {
-            sum += num % 10;
-            num /= 10;
-        }
-
-        return sum;
-    }
+package conjecture;
+
+// The following program is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
+
+import java.util.InputMismatchException;
+
+public class Main {
+    private static final int SUCCESS = 0;
+    private static final int FAIL = 1;
+    private static final int INVALID_INPUT = 2;
+
+    public static void main(String[] args) {
+        try {
+            int max = Integer.parseInt(args[0]);
+
+            if (getCounterexample(max)) {
+                System.exit(FAIL);
+            } else {
+                System.exit(SUCCESS);
+            }
+        } catch (InputMismatchException error) {
+            System.exit(INVALID_INPUT);
+        }
+
+    }
+
+    private static Boolean getCounterexample(int max) {
+        int[] sum = getSums(max);
+
+        for (int a = 0; a <= max; a++)
+            for (int b = a; b <= max; b++) {
+                int diff = sum[a + b] - (sum[a] + sum[b]);
+
+                if (diff % 9 != 0)
+                    return true;
+            }
+
+        return false;
+    }
+
+    private static int[] getSums(int max) {
+        int maxRange = 2 * (max + 1);
+        int[] sums = new int[maxRange];
+
+        for (int i = 0; i < maxRange; i++)
+            sums[i] = sumDigits(i);
+
+        return sums;
+    }
+
+    private static int sumDigits(int n) {
+        int num = Math.abs(n), sum = 0;
+
+        while (num > 0) {
+            sum += num % 10;
+            num /= 10;
+        }
+
+        return sum;
+    }
 } 
\ No newline at end of file

diff --git a/Kotlin/.gitignore b/Kotlin/.gitignore
@@ -1,2 +1,2 @@
-.idea
+.idea
 out 
\ No newline at end of file

diff --git a/Kotlin/Kotli.iml b/Kotlin/Kotli.iml
@@ -1,12 +1,12 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<module type="JAVA_MODULE" version="4">
-  <component name="NewModuleRootManager" inherit-compiler-output="true">
-    <exclude-output />
-    <content url="file://$MODULE_DIR$">
-      <sourceFolder url="file://$MODULE_DIR$/src" isTestSource="false" />
-    </content>
-    <orderEntry type="inheritedJdk" />
-    <orderEntry type="sourceFolder" forTests="false" />
-    <orderEntry type="library" name="KotlinJavaRuntime" level="project" />
-  </component>
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="JAVA_MODULE" version="4">
+  <component name="NewModuleRootManager" inherit-compiler-output="true">
+    <exclude-output />
+    <content url="file://$MODULE_DIR$">
+      <sourceFolder url="file://$MODULE_DIR$/src" isTestSource="false" />
+    </content>
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+    <orderEntry type="library" name="KotlinJavaRuntime" level="project" />
+  </component>
 </module> 
\ No newline at end of file

diff --git a/Kotlin/src/main.kt b/Kotlin/src/main.kt
@@ -1,57 +1,57 @@
-package conjecture
-
-import kotlin.math.absoluteValue
-import kotlin.system.exitProcess
-
-// The following program is a simple test for the following conjecture:
-
-// Let S: N -> N be the sum of the digits of a positive integer.
-// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
-
-fun main(args: Array<String>) {
-    try {
-        val max = args[0].toInt()
-
-        if (counterexample(max)) exitProcess(1)
-        else exitProcess(0)
-
-    } catch (_: Exception) {
-        exitProcess(2)
-    }
-}
-
-internal fun counterexample(max: Int): Boolean {
-    val sum = sums(max)
-
-    for (a in 0..max)
-        for (b in a..max) {
-            val diff = sum[a + b] - sum[a] - sum[b]
-
-            if (diff % 9 != 0)
-                return true
-        }
-
-    return false
-}
-
-fun sums (max: Int): IntArray {
-    val maxRange = 2 * max + 1
-    val sums = IntArray(maxRange)
-
-    for (i in 0 until maxRange)
-        sums[i] = sumDigits(i)
-
-    return sums
-}
-
-fun sumDigits(n: Int): Int {
-    var sum = 0
-    var num = n.absoluteValue
-
-    while (num > 0) {
-        sum += num % 10
-        num /= 10
-    }
-
-    return sum
+package conjecture
+
+import kotlin.math.absoluteValue
+import kotlin.system.exitProcess
+
+// The following program is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
+
+fun main(args: Array<String>) {
+    try {
+        val max = args[0].toInt()
+
+        if (counterexample(max)) exitProcess(1)
+        else exitProcess(0)
+
+    } catch (_: Exception) {
+        exitProcess(2)
+    }
+}
+
+internal fun counterexample(max: Int): Boolean {
+    val sum = sums(max)
+
+    for (a in 0..max)
+        for (b in a..max) {
+            val diff = sum[a + b] - sum[a] - sum[b]
+
+            if (diff % 9 != 0)
+                return true
+        }
+
+    return false
+}
+
+fun sums (max: Int): IntArray {
+    val maxRange = 2 * max + 1
+    val sums = IntArray(maxRange)
+
+    for (i in 0 until maxRange)
+        sums[i] = sumDigits(i)
+
+    return sums
+}
+
+fun sumDigits(n: Int): Int {
+    var sum = 0
+    var num = n.absoluteValue
+
+    while (num > 0) {
+        sum += num % 10
+        num /= 10
+    }
+
+    return sum
 } 
\ No newline at end of file

diff --git a/README.md b/README.md
@@ -1,28 +1,30 @@
-# A Conjecture of Mine
-An exercise on _polyglossy_. The same problem solved on multiple languages.
-
-## The Problem - Mathematicians Version
-Let <img src="https://latex.codecogs.com/svg.latex?S:&space;\mathbb{N}\rightarrow&space;\mathbb{N}"/> be the sum of the digits of a positive integer in a [_base 10 positional number system_](https://en.wikipedia.org/wiki/Positional_notation). We have:
-
-<img src="https://latex.codecogs.com/svg.latex?\forall&space;a,&space;b&space;\in&space;\mathbb{N},&space;S_{a&space;&plus;&space;b}&space;\equiv&space;S_a&space;&plus;&space;S_b&space;\;\(\textup{mod}\;&space;9&space;\)"/>
-
-### Addendum
-This conjecture can be generalized for any _positional number system_. Check out `proof.pdf` for more information.
-
-## The Problem - Programmers Verison
-
-Let `S(n: uint) -> uint` be the sum of the digits of `n` in [_base 10_](https://en.wikipedia.org/wiki/Decimal). Then, for all `a` and `b` of type `uint`, `S(a + b) - ( S(a) + S(b) ) % 9 == 0`.
-
-## Performance
-The conjecture was [proved by exhaustion](https://en.wikipedia.org/wiki/Proof_by_exhaustion) for the interval <img src="https://latex.codecogs.com/svg.latex?[0,&space;10^4]"/> in multiple language implementations. The performance of each language was then avaliated as the following:
-
-|Language      |Milliseconds|
-|--------------|------------|
-|**Rust**      |103         |
-|**C**         |113         | 
-|**Kotlin**    |137         |
-|**Go**        |155         |
-|**JavaScript**|656         |
-|**Ruby**      |9850        |
-|**Python**    |16032       |
-|**Haskell**   |28365       |
+# A Conjecture of Mine
+An exercise on _polyglossy_. The same problem solved on multiple languages.
+
+## The Problem - Mathematicians Version
+Let <img src="https://latex.codecogs.com/svg.latex?S:&space;\mathbb{N}\rightarrow&space;\mathbb{N}"/> be the sum of the digits of a positive integer in a _[base 10 positional number system](https://en.wikipedia.org/wiki/Positional_notation)_. We have:
+
+<img src="https://latex.codecogs.com/svg.latex?\forall&space;a,&space;b&space;\in&space;\mathbb{N},&space;S_{a&space;&plus;&space;b}&space;\equiv&space;S_a&space;&plus;&space;S_b&space;\;\(\textup{mod}\;&space;9&space;\)"/>
+
+### Addendum
+This conjecture can be generalized for any _positional number system_. Check out `proof.pdf` for more information.
+
+## The Problem - Programmers Verison
+
+Let `S(n: uint) -> uint` be the sum of the digits of `n` in _[base 10](https://en.wikipedia.org/wiki/Decimal)_. Then, for all `a` and `b` of type `uint`, `S(a + b) - ( S(a) + S(b) ) % 9 == 0`.
+
+## Performance
+The conjecture was [proved by exhaustion](https://en.wikipedia.org/wiki/Proof_by_exhaustion) for the interval <img src="https://latex.codecogs.com/svg.latex?[0,&space;10^4]"/> in multiple language implementations. The performance of each language was then avaliated as the following _(*)_:
+
+|Language      |Milliseconds|
+|--------------|------------|
+|**Rust**      |103         |
+|**C**         |113         | 
+|**Kotlin**    |137         |
+|**Go**        |155         |
+|**JavaScript**|656         |
+|**Ruby**      |9850        |
+|**Python**    |16032       |
+|**Haskell**   |28365       |
+
+_* out of date_

diff --git a/Rust/.gitignore b/Rust/.gitignore
@@ -1,2 +1,2 @@
-/target
-**/*.rs.bk
+/target
+**/*.rs.bk

diff --git a/Rust/Cargo.lock b/Rust/Cargo.lock
@@ -1,3 +1,5 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
 [[package]]
 name = "digital_sum"
 version = "0.1.0"

diff --git a/Rust/Cargo.toml b/Rust/Cargo.toml
@@ -1,7 +1,7 @@
-[package]
-name = "digital_sum"
-version = "0.1.0"
-authors = ["Gark Garcia <37553739+GarkGarcia@users.noreply.github.com>"]
-
-[dependencies]
+[package]
+name = "digital_sum"
+version = "0.1.0"
+authors = ["Gark Garcia <37553739+GarkGarcia@users.noreply.github.com>"]
+
+[dependencies]
 num_cpus = "1.0" 
\ No newline at end of file

diff --git a/Rust/src/main.rs b/Rust/src/main.rs
@@ -1,118 +1,118 @@
-// The following program is a simple test for the following conjecture:
-
-// Let S: N -> N be the sum of the digits of a positive integer.
-// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
-
-extern crate num_cpus;
-
-use std::{env, process, thread, sync::{Arc, mpsc::{self, Sender, Receiver}}};
-
-const SUCCESS: i32 = 0;
-const FAIL: i32 = 1;
-const INVALID_INPUT: i32 = 2;
-
-fn main() {
-    let args: Vec<String> = env::args().collect();
-
-    if args.len() > 1 {
-        let max_str = args[1].clone();
-
-        // Assign the correct number of threads to run the application with
-        // The default is the number of cores in the machine
-        let n_cores = num_cpus::get_physical();
-        let n_threads = if args.len() <= 2 { n_cores } else {
-            match args[2].trim().parse::<usize>() {
-                Ok(n_arg) => std::cmp::min(n_arg, n_cores),
-                Err(_) => n_cores
-            }
-        };
-
-        match max_str.trim().parse::<usize>() {
-            Ok(max) => if get_countrexpl(max, n_threads) {
-                process::exit(FAIL);
-            } else {
-                process::exit(SUCCESS);
-            }, 
-            Err(_) => process::exit(INVALID_INPUT)
-        }
-    } else {
-        process::exit(INVALID_INPUT);
-    }
-}
-
-/// Distributes calculations across threads and collect the results
-fn get_countrexpl(max: usize, n_threads: usize) -> bool {
-    let sums_cache = Arc::new(get_sums(max));
-
-    if n_threads > 1 {
-        let (coutexpl_sender, coutexpl_reciever): (Sender<bool>, Receiver<bool>) = mpsc::channel();
-        let mut child_threads = Vec::with_capacity(n_threads);
-
-        for i in 0..n_threads {
-            let thread_countr_sd = coutexpl_sender.clone();
-            let thread_sums = sums_cache.clone();
-
-            // By separating the interval [0..max] in subsections with the form [i + 0n, i + 1n, i + 2n, ...] we can ensure that every
-            // value will get tested on a single thread and that all threads will perform roughtly the same number of operations
-            let thread_range = (i..max).step_by(n_threads);
-
-            let child = thread::spawn(move || thread_countr_sd.send(get_iter_countrexpl(thread_range, thread_sums, max))
-                .expect(&format!("Thread n°{} was unable to sent a message trought the channel", i)));
-            
-            child_threads.push(child);
-            if let Ok(true) = coutexpl_reciever.recv() {
-                return true;
-            }
-        }
-
-        for child in child_threads {
-            child.join().expect("Child thread panicked");
-        }
-
-        false
-    } else {
-        get_iter_countrexpl(0..max, sums_cache, max)
-    }
-}
-
-/// Search for counterexamples among the items of a specif iterator.
-fn get_iter_countrexpl<I: IntoIterator<Item = usize>>(
-    iter: I,
-    sums_cache: Arc<Vec<isize>>,
-    max: usize
-) -> bool {
-    for a in iter {
-        for b in a..max {
-            let diff = sums_cache[a + b] - sums_cache[a] - sums_cache[b];
-
-            if diff % 9 != 0 {
-                return true;
-            }
-        }
-    }
-
-    false
-}
-
-fn sum_digits(n: usize) -> isize {
-    let mut sum = 0;
-    let mut part = n;
-
-    while part != 0 {
-        sum += part % 10;
-        part /= 10;
-    }
-
-    sum as isize
-}
-
-fn get_sums(max: usize) -> Vec<isize> {
-    let range_max = 2 * (max + 1);
-    let mut output = Vec::with_capacity(range_max);
-
-    for i in 0..range_max {
-        output.push(sum_digits(i));
-    }
-
-    output
-}-
\ No newline at end of file
+// The following program is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
+
+extern crate num_cpus;
+
+use std::{env, process, thread, sync::{Arc, mpsc::{self, Sender, Receiver}}};
+
+const SUCCESS: i32 = 0;
+const FAIL: i32 = 1;
+const INVALID_INPUT: i32 = 2;
+
+fn main() {
+    let args: Vec<String> = env::args().collect();
+
+    if args.len() > 1 {
+        let max_str = args[1].clone();
+
+        // Assign the correct number of threads to run the application with
+        // The default is the number of cores in the machine
+        let n_cores = num_cpus::get_physical();
+        let n_threads = if args.len() <= 2 { n_cores } else {
+            match args[2].trim().parse::<usize>() {
+                Ok(n_arg) => std::cmp::min(n_arg, n_cores),
+                Err(_) => n_cores
+            }
+        };
+
+        match max_str.trim().parse::<usize>() {
+            Ok(max) => if get_countrexpl(max, n_threads) {
+                process::exit(FAIL);
+            } else {
+                process::exit(SUCCESS);
+            }, 
+            Err(_) => process::exit(INVALID_INPUT)
+        }
+    } else {
+        process::exit(INVALID_INPUT);
+    }
+}
+
+/// Distributes calculations across threads and collect the results
+fn get_countrexpl(max: usize, n_threads: usize) -> bool {
+    let sums_cache = Arc::new(get_sums(max));
+
+    if n_threads > 1 {
+        let (coutexpl_sender, coutexpl_reciever): (Sender<bool>, Receiver<bool>) = mpsc::channel();
+        let mut child_threads = Vec::with_capacity(n_threads);
+
+        for i in 0..n_threads {
+            let thread_countr_sd = coutexpl_sender.clone();
+            let thread_sums = sums_cache.clone();
+
+            // By separating the interval [0..max] in subsections with the form [i + 0n, i + 1n, i + 2n, ...] we can ensure that every
+            // value will get tested on a single thread and that all threads will perform roughtly the same number of operations
+            let thread_range = (i..max).step_by(n_threads);
+
+            let child = thread::spawn(move || thread_countr_sd.send(get_iter_countrexpl(thread_range, thread_sums, max))
+                .expect(&format!("Thread n°{} was unable to sent a message trought the channel", i)));
+            
+            child_threads.push(child);
+            if let Ok(true) = coutexpl_reciever.recv() {
+                return true;
+            }
+        }
+
+        for child in child_threads {
+            child.join().expect("Child thread panicked");
+        }
+
+        false
+    } else {
+        get_iter_countrexpl(0..max, sums_cache, max)
+    }
+}
+
+/// Search for counterexamples among the items of a specif iterator.
+fn get_iter_countrexpl<I: IntoIterator<Item = usize>>(
+    iter: I,
+    sums_cache: Arc<Vec<isize>>,
+    max: usize
+) -> bool {
+    for a in iter {
+        for b in a..max {
+            let diff = sums_cache[a + b] - sums_cache[a] - sums_cache[b];
+
+            if diff % 9 != 0 {
+                return true;
+            }
+        }
+    }
+
+    false
+}
+
+fn sum_digits(n: usize) -> isize {
+    let mut sum = 0;
+    let mut part = n;
+
+    while part != 0 {
+        sum += part % 10;
+        part /= 10;
+    }
+
+    sum as isize
+}
+
+fn get_sums(max: usize) -> Vec<isize> {
+    let range_max = 2 * (max + 1);
+    let mut output = Vec::with_capacity(range_max);
+
+    for i in 0..range_max {
+        output.push(sum_digits(i));
+    }
+
+    output
+}

diff --git a/hla/conjecture.hla b/hla/conjecture.hla
@@ -1,129 +1,129 @@
-program conjecture;
-
-	#includeonce( "stdlib.hhf" )
-	#includeonce( "w32\win32.hhf")
-	
-	?@nodisplay := true;
-	?@noalignstack := true;
-
-// This program is a simple test for the following conjecture:
-
-// Let S: N -> N be the sum of the digits of a positive integer.
-// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
-
-// data segments
-storage
-	max			:uns32;
-	sumAB		:uns32;
-	sumA		:uns32;
-	sumB		:uns32;
-	timeStart	:dword;
-	timeEnd		:dword;
-	
-static
-	err			:boolean := false;
-	
-
-// input eax = number to sum
-// returns sum in ebx
-procedure sum_digits;
-
-	// don't build a stack frame for this procedure
-	@nodisplay; @noframe;
-
-begin sum_digits;
-	
-	mov( 10, ecx );
-	xor( ebx, ebx );
-	while( eax ) do
-		xor( edx, edx );
-		div( ecx );
-		add( edx, ebx );
-	endwhile;
-	ret;
-
-end sum_digits;
-
-
-
-begin conjecture;
-
-	// read an unsigned integer from the user
-	forever
-		try
-			stdout.put ("enter an unsigned integer :>" );
-			stdin.getu32();
-			mov( eax, max );
-			break;
-		anyexception;
-			stdout.newln();
-			continue;
-		endtry;
-	endfor;
-	
-	
-	
-	stdout.put ("Loading ..." nl );
-	w.GetTickCount();
-	mov( eax, timeStart );
-	
-	for( xor(esi, esi); esi <= max; inc( esi ) ) do
-		
-		// outer loop esi = 0 to max iterations
-		
-		for( mov(esi, edi); edi <= max; inc( edi ) ) do
-			
-			// inner loop. edi = esi to max iterations
-			
-			// get S(a+b)
-			mov( esi, eax );
-			add( edi, eax );
-			call sum_digits;
-			mov( ebx, sumAB );
-			
-			// get S(a)
-			mov( esi, eax );
-			call sum_digits;
-			mov( ebx, sumA );
-			
-			// get S(b)
-			mov( edi, eax );
-			call sum_digits;
-			mov( ebx, sumB );
-			
-			// get S(a+b) - S(a) - S(b)
-			mov( sumAB, eax );
-			sub( sumA, eax );
-			sub( sumB, eax );
-			
-			// sign extend into edx
-			cdq();
-			mov( 9, ecx );
-			idiv( ecx );	// signed division of edx:eax
-			test( edx, edx ); // is remainder zero?
-			if( @nz ) then
-				// if remainder is not zero, the conjecture is false
-				stdout.put ("Conjecture is disproved, here is the counter example :", (type uns32 eax), nl );
-				mov( true, err );
-				break;
-			endif;
-		endfor;
-		
-		breakif( err );
-		
-	endfor;
-	
-	// if we get here, we looped through all the values and the
-	// conjecture is proved.
-	if( !err ) then
-		
-		w.GetTickCount();
-		mov( eax, timeEnd );
-		mov( timeEnd, eax );
-		sub( timeStart, eax );
-		stdout.put("Loaded in : ", (type uns32 eax), "ms,  [1 Thread, no preprocessing]", nl);		
-		stdout.put ("The conjecture is proved for all natural numbers smaller or equals to ", max, "!", nl );
-
-	endif;
-
-end conjecture;
+program conjecture;
+
+	#includeonce( "stdlib.hhf" )
+	#includeonce( "w32\win32.hhf")
+	
+	?@nodisplay := true;
+	?@noalignstack := true;
+
+// This program is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+// data segments
+storage
+	max			:uns32;
+	sumAB		:uns32;
+	sumA		:uns32;
+	sumB		:uns32;
+	timeStart	:dword;
+	timeEnd		:dword;
+	
+static
+	err			:boolean := false;
+	
+
+// input eax = number to sum
+// returns sum in ebx
+procedure sum_digits;
+
+	// don't build a stack frame for this procedure
+	@nodisplay; @noframe;
+
+begin sum_digits;
+	
+	mov( 10, ecx );
+	xor( ebx, ebx );
+	while( eax ) do
+		xor( edx, edx );
+		div( ecx );
+		add( edx, ebx );
+	endwhile;
+	ret;
+
+end sum_digits;
+
+
+
+begin conjecture;
+
+	// read an unsigned integer from the user
+	forever
+		try
+			stdout.put ("enter an unsigned integer :>" );
+			stdin.getu32();
+			mov( eax, max );
+			break;
+		anyexception;
+			stdout.newln();
+			continue;
+		endtry;
+	endfor;
+	
+	
+	
+	stdout.put ("Loading ..." nl );
+	w.GetTickCount();
+	mov( eax, timeStart );
+	
+	for( xor(esi, esi); esi <= max; inc( esi ) ) do
+		
+		// outer loop esi = 0 to max iterations
+		
+		for( mov(esi, edi); edi <= max; inc( edi ) ) do
+			
+			// inner loop. edi = esi to max iterations
+			
+			// get S(a+b)
+			mov( esi, eax );
+			add( edi, eax );
+			call sum_digits;
+			mov( ebx, sumAB );
+			
+			// get S(a)
+			mov( esi, eax );
+			call sum_digits;
+			mov( ebx, sumA );
+			
+			// get S(b)
+			mov( edi, eax );
+			call sum_digits;
+			mov( ebx, sumB );
+			
+			// get S(a+b) - S(a) - S(b)
+			mov( sumAB, eax );
+			sub( sumA, eax );
+			sub( sumB, eax );
+			
+			// sign extend into edx
+			cdq();
+			mov( 9, ecx );
+			idiv( ecx );	// signed division of edx:eax
+			test( edx, edx ); // is remainder zero?
+			if( @nz ) then
+				// if remainder is not zero, the conjecture is false
+				stdout.put ("Conjecture is disproved, here is the counter example :", (type uns32 eax), nl );
+				mov( true, err );
+				break;
+			endif;
+		endfor;
+		
+		breakif( err );
+		
+	endfor;
+	
+	// if we get here, we looped through all the values and the
+	// conjecture is proved.
+	if( !err ) then
+		
+		w.GetTickCount();
+		mov( eax, timeEnd );
+		mov( timeEnd, eax );
+		sub( timeStart, eax );
+		stdout.put("Loaded in : ", (type uns32 eax), "ms,  [1 Thread, no preprocessing]", nl);		
+		stdout.put ("The conjecture is proved for all natural numbers smaller or equals to ", max, "!", nl );
+
+	endif;
+
+end conjecture;

diff --git a/script.js b/script.js
@@ -1,39 +1,39 @@
-// This script is a simple test for the following conjecture:
-
-// Let S: N -> N be the sum of the digits of a positive integer.
-// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
-
-function sumDigits() {
-    if (isNaN(this) || !isFinite(this) || !this)
-        throw new TypeError
-
-    let parc = Math.abs(this), sum = 0;
-
-    while (parc > 0) {
-        sum += parc % 10;
-        parc = Math.floor(parc / 10);
-    }
-
-    return sum;
-}
-
-function getSums(max) {
-    const output = [], maxRange = 2 * (max + 1);
-    
-    for (let i = 0; i <= maxRange; i++)
-        output.push(sumDigits(i));
-
-    return output;
-}
-
-export function getCounterExp(max) {
-    const sums = getSums(max);
-
-    for (let a = 1; a <= max; a++)
-        for (let b = a; b <= max; b++) {
-            const diff = sums[a + b] - (sums[a] + sums[b]);
-            if (diff % 9 !== 0) return true;
-        }
-
-    return false;
-}-
\ No newline at end of file
+// This script is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+function sumDigits(n) {
+    if (isNaN(n) || !isFinite(n) || !n)
+        throw new TypeError
+
+    let parc = Math.abs(n), sum = 0;
+
+    while (parc > 0) {
+        sum += parc % 10;
+        parc = Math.floor(parc / 10);
+    }
+
+    return sum;
+}
+
+function getSums(max) {
+    const output = [], maxRange = 2 * (max + 1);
+    
+    for (let i = 0; i <= maxRange; i++)
+        output.push(sumDigits(i));
+
+    return output;
+}
+
+export function getCounterExp(max) {
+    const sums = getSums(max);
+
+    for (let a = 1; a <= max; a++)
+        for (let b = a; b <= max; b++) {
+            const diff = sums[a + b] - (sums[a] + sums[b]);
+            if (diff % 9 !== 0) return true;
+        }
+
+    return false;
+}

diff --git a/script.pl b/script.pl
@@ -1,29 +1,29 @@
-% The following script is a simple test for the following conjecture:
-
-% Let S: N -> N be the sum of the digits of a positive integer.
-% For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
-
-sum_digits(X, Y) :- sum_digits_acc(X, 0, Y).
-
-sum_digits_acc(X, A, Y) :- X < 10, !, Y is A + X.
-sum_digits_acc(X, A, Y) :-
-    Q  = X div 10,
-    R  = X mod 10,
-    A2 = A + R,
-    sum_digits_acc(Q, A2, Y).
-
-test_pair(A, B) :-
-    R  = 0,
-    AB = A + B,
-    sum_digits(A, SA),
-    sum_digits(B, SB),
-    sum_digits(AB, SC),
-    SAB = SA + SB,
-    D   = SC - SAB,
-    R =:= D mod 9.
-
-iter(A, B) :-
-    forall(between(0, B, X), test_pair(A, X)).
-
-conjecture(M) :-
+% The following script is a simple test for the following conjecture:
+
+% Let S: N -> N be the sum of the digits of a positive integer.
+% For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
+
+sum_digits(X, Y) :- sum_digits_acc(X, 0, Y).
+
+sum_digits_acc(X, A, Y) :- X < 10, !, Y is A + X.
+sum_digits_acc(X, A, Y) :-
+    Q  = X div 10,
+    R  = X mod 10,
+    A2 = A + R,
+    sum_digits_acc(Q, A2, Y).
+
+test_pair(A, B) :-
+    R  = 0,
+    AB = A + B,
+    sum_digits(A, SA),
+    sum_digits(B, SB),
+    sum_digits(AB, SC),
+    SAB = SA + SB,
+    D   = SC - SAB,
+    R =:= D mod 9.
+
+iter(A, B) :-
+    forall(between(0, B, X), test_pair(A, X)).
+
+conjecture(M) :-
     forall(between(0, M, X), iter(X, X)). 
\ No newline at end of file

diff --git a/script.py b/script.py
@@ -1,34 +1,34 @@
-# This script is a simple test for the following conjecture:
-
-# Let S: N -> N be the sum of the digits of a positive integer.
-# For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
-
-def sum_digits(n: int) -> int:
-    parc = abs(n)
-    sum_d = 0
-
-    while parc > 0:
-        sum_d += parc % 10
-        parc //= 10
-
-    return sum_d
-
-def get_sums(max: int) -> list:
-    output = []
-
-    for i in range(2 * max):
-        output.append(sum_digits(i))
-
-    return output
-
-def get_counterexmpl(max: int) -> bool:
-    sums = get_sums(max)
-
-    for a in range(max + 1):
-        for b in range(a, max + 1):
-            diff = sums[a + b] - sums[a] - sums[b]
-
-            if not diff % 9 == 0:
-                return True
-    
-    return False
+# This script is a simple test for the following conjecture:
+
+# Let S: N -> N be the sum of the digits of a positive integer.
+# For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+def sum_digits(n: int) -> int:
+    parc = abs(n)
+    sum_d = 0
+
+    while parc > 0:
+        sum_d += parc % 10
+        parc //= 10
+
+    return sum_d
+
+def get_sums(max: int) -> list:
+    output = []
+
+    for i in range(2 * max):
+        output.append(sum_digits(i))
+
+    return output
+
+def get_counterexmpl(max: int) -> bool:
+    sums = get_sums(max)
+
+    for a in range(max + 1):
+        for b in range(a, max + 1):
+            diff = sums[a + b] - sums[a] - sums[b]
+
+            if not diff % 9 == 0:
+                return True
+    
+    return False

diff --git a/script.rb b/script.rb
@@ -1,43 +1,43 @@
-# This script is a simple test for the following conjecture:
-
-# Let S: N -> N be the sum of the digits of a positive integer.
-# For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
-
-def sumDigits(i)
-    part = i.abs()
-    sum = 0
-
-    while part > 0
-        d, r = part.divmod(10)
-        sum += r
-        part = d
-    end
-
-    return sum
-end
-
-def getSums(max)
-    output = []
-    
-    for i in 0..((max + 1) * 2)
-        output << sumDigits(i)
-    end
-
-    return output
-end
-
-def get_counterexpl(max)
-    sums = getSums(max)
-
-    for a in (0..max)
-        for b in (a..max)
-            diff = sums[a + b] - sums[a] - sums[b]
-
-            if diff % 9 != 0
-                return true
-            end
-        end
-    end
-
-    return false
+# This script is a simple test for the following conjecture:
+
+# Let S: N -> N be the sum of the digits of a positive integer.
+# For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+def sumDigits(i)
+    part = i.abs()
+    sum = 0
+
+    while part > 0
+        d, r = part.divmod(10)
+        sum += r
+        part = d
+    end
+
+    return sum
+end
+
+def getSums(max)
+    output = []
+    
+    for i in 0..((max + 1) * 2)
+        output << sumDigits(i)
+    end
+
+    return output
+end
+
+def get_counterexpl(max)
+    sums = getSums(max)
+
+    for a in (0..max)
+        for b in (a..max)
+            diff = sums[a + b] - sums[a] - sums[b]
+
+            if diff % 9 != 0
+                return true
+            end
+        end
+    end
+
+    return false
 end 
\ No newline at end of file

diff --git a/x86/PROGRAM.ASM b/x86/PROGRAM.ASM
@@ -1,413 +1,413 @@
-.model tiny
-
-.stack 1000h
-
-.data
-        input      db 8 DUP(0)
-        invalid    db "' is not a natural number!", 0dh, 0ah, 0dh, 0ah, "$"
-        too_big    db " is too big!", 0dh, 0ah, 0dh, 0ah, "$"
-
-        max        dw 0
-        a          dw 0
-        b          dw 0
-        sumAB      dw 0
-        sumA       dw 0
-        sumB       dw 0
-
-        sums_cache dw 25000 DUP(0)
-
-        start_time dw 0
-        end_time   dw 0
-
-        proof      db 0dh, 0ah, "The conjecture is proved for all natural numbers smaller or equals to $"
-        counter    db 0dh, 0ah, "The conjecture is disproved! Here's a counterexample: ($"
-        loading    db 0dh, 0ah, "LOADING. . .$"
-        loaded     db 0dh, 0ah, "LOADED. . . in $"
-
-        intro1     db 0dh, 0ah, "This program is a simple test for the following conjecture:", 0dh, 0ah, "$"
-        intro2     db 0dh, 0ah, "Let S: N -> N be the sum of the digits of a positive integer.", 0dh, 0ah, "$"
-        intro3     db "For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.", 0dh, 0ah, "$"
-        intro4     db 0dh, 0ah, "What value would you like to test the conjecture for? $"
-
-.code
-        org 100h
-
-start:
-        mov ax, @data
-        mov ds, ax
-
-        ; Print the intro messages to the screen
-        mov ah, 9h
-        mov dx, offset intro1
-        int 21h
-        mov dx, offset intro2
-        int 21h
-        mov dx, offset intro3
-        int 21h
-        mov dx, offset intro4
-        int 21h
-
-        call read_uint ; Retrieve user input  
-
-        ; Set the start_time variable
-        mov si, offset start_time
-        call get_time
-
-        mov ah, 9h
-        mov dx, offset loading
-        int 21h
-
-        call cache_sums
-        call iter
-
-read_uint:
-        ; Load the user input into the input
-        mov ax, cs
-        mov ds, ax
-        mov input[0], 6 ; Configure the input length
-        mov dx, offset input
-        mov ah, 0ah
-        int 21h
-
-        ; Print '\n'
-        mov ah, 2h
-        mov dx, 0dh
-        int 21h
-        mov dx, 0ah
-        int 21h
-
-        ; Move si to the to adress of the first character in the input
-        mov si, offset input
-        add si, 2
-
-        mov ax, 0 ; Initialize the register where the result will be stored
-        mov cx, 1 ; Initialize a counter
-
-read_loop:
-        mov bx, 0 ; Clear bx
-        mov bl, [si] ; Read a character into bx
-        inc cx ; Increment the counter
-        inc si ; Increment the source index
-
-        ; Check if it's a numeric character
-        cmp bl, 30h
-        jb short invalid_input
-        cmp bl, 39h
-        ja short invalid_input
-
-        ; Convert the character code into a decimal digit
-        sub bl, 30h
-
-        ; ax = ax * 10 + bx
-        push cx
-        mov cx, 10
-        mul cx
-        pop cx
-        add ax, bx
-
-        cmp ax, 12500
-        ja short input_too_big
-
-        ; Jump if the counter is still smaller than the input length
-        cmp cl, input[1]
-        jbe short read_loop
-
-        mov max, ax
-        ret
-
-invalid_input:
-        mov ah, 2h
-
-        ; Print '\''
-        ;mov dx, 0ah
-        ;int 21
-        mov dx, 27h
-        int 21
-
-        mov si, offset input
-        call print_buffer
-
-        ; Print the rest of the message
-        mov ah, 9h
-        mov dx, offset invalid
-        int 21h
-
-        call quit
-        ret
-
-input_too_big:
-        mov si, offset input
-        call print_buffer
-
-        mov ah, 9h
-        mov dx, offset too_big
-        int 21h
-
-        call quit
-        ret
-
-cache_sums:
-        mov si, offset sums_cache
-
-        mov ax, max
-        mov bx, 2
-        mul bx
-        mov bx, ax
-
-        mov ax, 0
-cache_sums_loop:
-        push bx
-        push ax
-        call sum_digits
-        mov [si], bx
-
-        pop ax
-        add si, 2
-        inc ax
-
-        pop bx
-        cmp ax, bx
-        jb short cache_sums_loop
-        ret
-
-; Prints the characters of a buffer referenced by si
-print_buffer:
-        mov bh, si[1]
-
-        add si, 2
-        mov ch, 0
-
-        mov ah, 2h
-print_buffer_loop:
-        mov dl, [si]
-        int 21h
-
-        inc ch
-        inc si
-
-        cmp ch, bh
-        jb short print_buffer_loop
-        ret
-
-; Iterate a from 0 to max
-iter:
-        mov ax, a
-        call test_num
-
-        inc ax
-        mov a, ax
-        cmp ax, max
-        jbe short iter
-
-        call proved
-
-; Iterate b from a to max
-test_num:
-        mov ax, a
-        mov b, ax
-
-test_loop:
-        call test_pair
-
-        inc b
-        mov ax, b
-        cmp ax, max
-        jbe short test_loop
-        ret        
-
-test_pair:
-        ; Calculate S(A + B) and store it in sumAB
-        mov si, offset sums_cache
-        add si, a
-        add si, b
-        mov ax, [si]
-        mov sumAB, ax
-        mov ax, si
-
-        ; Calculate S(A) and store it in sumA
-        mov si, offset sums_cache
-        add si, a
-        mov ax, [si]
-        mov sumA, ax
-
-        ; Calculate S(B) and store it in sumB
-        mov si, offset sums_cache
-        add si, b
-        mov ax, [si]
-        mov sumB, ax 
-
-
-        ; Calculate S(a + b) - S(a) - S(b) in ax
-        mov ax, sumAB
-        sub ax, sumA
-        sub ax, sumB
-
-        mov cx, 9 ; Set the devident to 9
-        mov dx, 0 ; Clear the register where the rest will be stored
-        div cx
-
-        cmp dx, 0
-        jne disproved
-
-        ret
-
-sum_digits:
-        mov cx, 10 ; Store the devident in cx
-        mov bx, 0 ; Clear the register where the result will be stored
-sum_loop:
-        mov dx, 0 ; Clear the rest of the division
-
-        div cx ; Divide ax by cx
-        add bx, dx ; Add the rest of the division ax/cx to bx
-
-        ; Loop until ax equals 0
-        cmp ax, 0
-        ja short sum_loop
-        ret
-
-proved:
-        call print_time
-
-        mov ah, 9h
-        mov dx, offset proof
-        int 21h
-
-        mov ax, max
-        call print_uint
-
-        ; Print '!\n'
-        mov ah, 2h
-        mov dx, '!'
-        int 21h
-        mov dx, 0ah
-        int 21h
-
-        call quit
-        ret
-
-disproved:
-        mov ah, 9h
-        mov dx, offset counter
-        int 21h
-
-        mov ax, a
-        call print_uint
-
-        ; Print ', '
-        mov ah, 2h
-        mov dx, ','
-        int 21h
-        mov dx, ' '
-        int 21h
-
-        mov ax, b
-        call print_uint
-
-        ; Print ')\n'
-        mov ah, 2h
-        mov dx, ')'
-        int 21h
-        mov dx, 0ah
-        int 21h
-
-        call quit
-        ret
-
-print_uint:
-        mov bx, 10
-        mov cx, 0
-
-print_uint_collect:
-        mov dx, 0
-        div bx
-        add dx, 30h
-
-        push dx
-        inc cx
-
-        cmp ax, 0
-        ja short print_uint_collect
-
-        mov ah, 2h
-
-print_uint_loop:
-        pop dx
-        int 21h
-        dec cx
-
-        cmp cx, 0
-        ja short print_uint_loop
-        ret
-
-print_time:
-        ; Set the end_time variable
-        mov si, offset end_time
-        call get_time
-
-        mov ah, 9h
-        mov dx, offset loaded
-        int 21h
-
-        ; Print the elepsed time in milliseconds
-        mov ax, end_time
-        sub ax, start_time
-        mov cx, 10
-        mul cx
-        call print_uint
-
-        ; Print 'ms\n'
-        mov ah, 2h
-        mov dx, 'm'
-        int 21h
-        mov dx, 's'
-        int 21h
-        mov dx, 0ah
-        int 21h
-        ret
-
-; Gets the current minute in centiseconds and stores it in [si]
-get_time:
-        ; Get system time
-        mov ah, 2ch
-        int 21h
-
-        ; Add the minutes
-        mov ax, 0
-        mov al, ch
-        mov bx, 6000
-        mul bx
-        mov [si], ax
-
-        ; Add the seconds
-        mov ax, 0
-        mov al, dh
-        mov bx, 100
-        mul bx
-        add [si], ax
-
-        ; Add the centiseconds
-        mov ax, 0
-        mov al, dl
-        add [si], ax
-
-        ret
-
-; Print decimal value in ax, and a '.' to separate them. This was created for debugging porposes.
-print_dot_dec:
-        push bx
-        push cx
-        push dx
-        push ax
-        call print_uint
-        mov dx, '.'
-        int 21h
-        pop ax    
-        pop dx
-        pop cx
-        pop bx
-        ret
-        
-quit:
-        mov ax, 4c00h
-        int 21h
-end start
+.model tiny
+
+.stack 1000h
+
+.data
+        input      db 8 DUP(0)
+        invalid    db "' is not a natural number!", 0dh, 0ah, 0dh, 0ah, "$"
+        too_big    db " is too big!", 0dh, 0ah, 0dh, 0ah, "$"
+
+        max        dw 0
+        a          dw 0
+        b          dw 0
+        sumAB      dw 0
+        sumA       dw 0
+        sumB       dw 0
+
+        sums_cache dw 25000 DUP(0)
+
+        start_time dw 0
+        end_time   dw 0
+
+        proof      db 0dh, 0ah, "The conjecture is proved for all natural numbers smaller or equals to $"
+        counter    db 0dh, 0ah, "The conjecture is disproved! Here's a counterexample: ($"
+        loading    db 0dh, 0ah, "LOADING. . .$"
+        loaded     db 0dh, 0ah, "LOADED. . . in $"
+
+        intro1     db 0dh, 0ah, "This program is a simple test for the following conjecture:", 0dh, 0ah, "$"
+        intro2     db 0dh, 0ah, "Let S: N -> N be the sum of the digits of a positive integer.", 0dh, 0ah, "$"
+        intro3     db "For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.", 0dh, 0ah, "$"
+        intro4     db 0dh, 0ah, "What value would you like to test the conjecture for? $"
+
+.code
+        org 100h
+
+start:
+        mov ax, @data
+        mov ds, ax
+
+        ; Print the intro messages to the screen
+        mov ah, 9h
+        mov dx, offset intro1
+        int 21h
+        mov dx, offset intro2
+        int 21h
+        mov dx, offset intro3
+        int 21h
+        mov dx, offset intro4
+        int 21h
+
+        call read_uint ; Retrieve user input  
+
+        ; Set the start_time variable
+        mov si, offset start_time
+        call get_time
+
+        mov ah, 9h
+        mov dx, offset loading
+        int 21h
+
+        call cache_sums
+        call iter
+
+read_uint:
+        ; Load the user input into the input
+        mov ax, cs
+        mov ds, ax
+        mov input[0], 6 ; Configure the input length
+        mov dx, offset input
+        mov ah, 0ah
+        int 21h
+
+        ; Print '\n'
+        mov ah, 2h
+        mov dx, 0dh
+        int 21h
+        mov dx, 0ah
+        int 21h
+
+        ; Move si to the to adress of the first character in the input
+        mov si, offset input
+        add si, 2
+
+        mov ax, 0 ; Initialize the register where the result will be stored
+        mov cx, 1 ; Initialize a counter
+
+read_loop:
+        mov bx, 0 ; Clear bx
+        mov bl, [si] ; Read a character into bx
+        inc cx ; Increment the counter
+        inc si ; Increment the source index
+
+        ; Check if it's a numeric character
+        cmp bl, 30h
+        jb short invalid_input
+        cmp bl, 39h
+        ja short invalid_input
+
+        ; Convert the character code into a decimal digit
+        sub bl, 30h
+
+        ; ax = ax * 10 + bx
+        push cx
+        mov cx, 10
+        mul cx
+        pop cx
+        add ax, bx
+
+        cmp ax, 12500
+        ja short input_too_big
+
+        ; Jump if the counter is still smaller than the input length
+        cmp cl, input[1]
+        jbe short read_loop
+
+        mov max, ax
+        ret
+
+invalid_input:
+        mov ah, 2h
+
+        ; Print '\''
+        ;mov dx, 0ah
+        ;int 21
+        mov dx, 27h
+        int 21
+
+        mov si, offset input
+        call print_buffer
+
+        ; Print the rest of the message
+        mov ah, 9h
+        mov dx, offset invalid
+        int 21h
+
+        call quit
+        ret
+
+input_too_big:
+        mov si, offset input
+        call print_buffer
+
+        mov ah, 9h
+        mov dx, offset too_big
+        int 21h
+
+        call quit
+        ret
+
+cache_sums:
+        mov si, offset sums_cache
+
+        mov ax, max
+        mov bx, 2
+        mul bx
+        mov bx, ax
+
+        mov ax, 0
+cache_sums_loop:
+        push bx
+        push ax
+        call sum_digits
+        mov [si], bx
+
+        pop ax
+        add si, 2
+        inc ax
+
+        pop bx
+        cmp ax, bx
+        jb short cache_sums_loop
+        ret
+
+; Prints the characters of a buffer referenced by si
+print_buffer:
+        mov bh, si[1]
+
+        add si, 2
+        mov ch, 0
+
+        mov ah, 2h
+print_buffer_loop:
+        mov dl, [si]
+        int 21h
+
+        inc ch
+        inc si
+
+        cmp ch, bh
+        jb short print_buffer_loop
+        ret
+
+; Iterate a from 0 to max
+iter:
+        mov ax, a
+        call test_num
+
+        inc ax
+        mov a, ax
+        cmp ax, max
+        jbe short iter
+
+        call proved
+
+; Iterate b from a to max
+test_num:
+        mov ax, a
+        mov b, ax
+
+test_loop:
+        call test_pair
+
+        inc b
+        mov ax, b
+        cmp ax, max
+        jbe short test_loop
+        ret        
+
+test_pair:
+        ; Calculate S(A + B) and store it in sumAB
+        mov si, offset sums_cache
+        add si, a
+        add si, b
+        mov ax, [si]
+        mov sumAB, ax
+        mov ax, si
+
+        ; Calculate S(A) and store it in sumA
+        mov si, offset sums_cache
+        add si, a
+        mov ax, [si]
+        mov sumA, ax
+
+        ; Calculate S(B) and store it in sumB
+        mov si, offset sums_cache
+        add si, b
+        mov ax, [si]
+        mov sumB, ax 
+
+
+        ; Calculate S(a + b) - S(a) - S(b) in ax
+        mov ax, sumAB
+        sub ax, sumA
+        sub ax, sumB
+
+        mov cx, 9 ; Set the devident to 9
+        mov dx, 0 ; Clear the register where the rest will be stored
+        div cx
+
+        cmp dx, 0
+        jne disproved
+
+        ret
+
+sum_digits:
+        mov cx, 10 ; Store the devident in cx
+        mov bx, 0 ; Clear the register where the result will be stored
+sum_loop:
+        mov dx, 0 ; Clear the rest of the division
+
+        div cx ; Divide ax by cx
+        add bx, dx ; Add the rest of the division ax/cx to bx
+
+        ; Loop until ax equals 0
+        cmp ax, 0
+        ja short sum_loop
+        ret
+
+proved:
+        call print_time
+
+        mov ah, 9h
+        mov dx, offset proof
+        int 21h
+
+        mov ax, max
+        call print_uint
+
+        ; Print '!\n'
+        mov ah, 2h
+        mov dx, '!'
+        int 21h
+        mov dx, 0ah
+        int 21h
+
+        call quit
+        ret
+
+disproved:
+        mov ah, 9h
+        mov dx, offset counter
+        int 21h
+
+        mov ax, a
+        call print_uint
+
+        ; Print ', '
+        mov ah, 2h
+        mov dx, ','
+        int 21h
+        mov dx, ' '
+        int 21h
+
+        mov ax, b
+        call print_uint
+
+        ; Print ')\n'
+        mov ah, 2h
+        mov dx, ')'
+        int 21h
+        mov dx, 0ah
+        int 21h
+
+        call quit
+        ret
+
+print_uint:
+        mov bx, 10
+        mov cx, 0
+
+print_uint_collect:
+        mov dx, 0
+        div bx
+        add dx, 30h
+
+        push dx
+        inc cx
+
+        cmp ax, 0
+        ja short print_uint_collect
+
+        mov ah, 2h
+
+print_uint_loop:
+        pop dx
+        int 21h
+        dec cx
+
+        cmp cx, 0
+        ja short print_uint_loop
+        ret
+
+print_time:
+        ; Set the end_time variable
+        mov si, offset end_time
+        call get_time
+
+        mov ah, 9h
+        mov dx, offset loaded
+        int 21h
+
+        ; Print the elepsed time in milliseconds
+        mov ax, end_time
+        sub ax, start_time
+        mov cx, 10
+        mul cx
+        call print_uint
+
+        ; Print 'ms\n'
+        mov ah, 2h
+        mov dx, 'm'
+        int 21h
+        mov dx, 's'
+        int 21h
+        mov dx, 0ah
+        int 21h
+        ret
+
+; Gets the current minute in centiseconds and stores it in [si]
+get_time:
+        ; Get system time
+        mov ah, 2ch
+        int 21h
+
+        ; Add the minutes
+        mov ax, 0
+        mov al, ch
+        mov bx, 6000
+        mul bx
+        mov [si], ax
+
+        ; Add the seconds
+        mov ax, 0
+        mov al, dh
+        mov bx, 100
+        mul bx
+        add [si], ax
+
+        ; Add the centiseconds
+        mov ax, 0
+        mov al, dl
+        add [si], ax
+
+        ret
+
+; Print decimal value in ax, and a '.' to separate them. This was created for debugging porposes.
+print_dot_dec:
+        push bx
+        push cx
+        push dx
+        push ax
+        call print_uint
+        mov dx, '.'
+        int 21h
+        pop ax    
+        pop dx
+        pop cx
+        pop bx
+        ret
+        
+quit:
+        mov ax, 4c00h
+        int 21h
+end start