a-conjecture-of-mine

 # 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 i
     part = i.abs()
     sum = 0
 
     while part > 0
         d, r = part.divmod 10
         sum += r
         part = d
     end
 
     sum
 end
 
 def get_sums max
     (0 .. 2 * max).map {|i| sum_digits i}
 end
 
 def counterexempl? max
     sums_cache = get_sums max
 
     for a in 0..max
         for b in a..max
             diff = sums_cache[a + b] - sums_cache[a] - sums_cache[b]
             return true if diff % 9 != 0
         end
     end
 
     false
 end