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## Homework Statement

If n is composite, prove that there exist a,b in Zn such that a and be are nonzero, but ab=0

## Homework Equations

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

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!