If n is composite, prove that there exist a,b in Zn such that a and be are nonzero, but ab=0
if a is congruent to b mod n, then n divides (a-b)
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
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 =)