a-conjecture-of-mine

 // 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.
 
 use std::{env, process};
 
 const SUCCESS: i32 = 0;
 const FAIL: i32 = 1;
 const INVALID_INPUT: i32 = 2;
 
 macro_rules! parse_arg {
     ($argv: expr) => {{
         match $argv.next().and_then(|s| s.trim().parse().ok()) {
             Some(n) => n,
             None    => process::exit(INVALID_INPUT)
         }
     }}
 }
 
 fn main() {
     let mut args = env::args();
     args.next();
 
     let max = parse_arg!(args);
 
     if counterexempl(max) {
         process::exit(FAIL);
     } else {
         process::exit(SUCCESS);
     }
 }
 
 fn counterexempl(max: usize) -> bool {
     let sums_cache = get_sums(max);
 
     for a in 0..max {
         for b in a..max {
             if (sums_cache[a + b] - sums_cache[a] - sums_cache[b]) % 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 mut output = Vec::with_capacity(2 * max);
 
     for n in 0..max * 2 {
         output.push(sum_digits(n));
     }
 
     output
 }