1. The problem statement, all variables and given/known data If n is composite, prove that there exist a,b in Zn such that a and be are nonzero, but ab=0 2. Relevant equations if a is congruent to b mod n, then n divides (a-b) 3. The attempt at a solution So this is what i have so far, please let me know if i am on the right track, and if i am then where would i go next? Suppose n is composite and a,b are in Zn where ab=0 which means, ab is congruent to 0(mod n) where n divides ab *this is where i get stuck, i'm thinking i have to say something about n having a unique prime number factorization, but i don't know how to show that in my proof... any help/hints would be great =) Thanks!