From Razzi: I've been having a hard time trying to solve the following problem and I was wondering if you could help me.
For any positive integer a let S(a) be the sum of its digits. Prove that a is divisible by 9 if and only if there exist a positive integer b such that S(a)=S(b)=S(a+b).
Answered by Chris Fisher and Harley Weston.
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