a-conjecture-of-mine

 package conjecture
 
 import kotlin.math.absoluteValue
 import kotlin.system.exitProcess
 import kotlin.collections.HashMap
 
 // 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.
 
 val OK = 0
 val FAIL = 1
 val INVALID_INPUT = 2
 
 fun main(args: Array<String>) {
     try {
         val max = args[0].toInt()
         if (max <= 0) throw IllegalArgumentException()
 
         val sumsCache = IntArray(2 * max + 1) { n -> sumDigits(n) }
 
         if (counterexample(max, sumsCache)) exitProcess(FAIL)
         else exitProcess(OK)
 
     } catch (_: Exception) {
         exitProcess(INVALID_INPUT)
     }
 }
 
 /**
  * Searches for a counterexample for the theorem in
  * `{(a, b) in N^2 | a <= max, b <= a}`.
  */
 fun counterexample(max: Int, sumsCache: IntArray): Boolean {
     for (a in 0..max)
         for (b in a..max) {
             val diff = sumsCache[a + b] - sumsCache[a] - sumsCache[b]
             if (diff % 9 != 0) return true
         }
 
     return false
 }
 
 /**
  * Calculates the sum of the digits of a positive integer.
  */
 fun sumDigits(n: Int): Int {
     var sum = 0
     var num = n
 
     while (num > 0) {
         sum += num % 10
         num /= 10
     }
 
     return sum
 }