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## Homework Statement

Prove that if A, a non zero element in Zn (integers mod n) is not a unit then A is a zero divisor in Zn.

## The Attempt at a Solution

[AB] does not equal 1 mod n for some A and all B in Zn

=> the element A is a multiple of n so n divides A because otherwise there should be a remainder of 1.

=> AB=0 for all B in Zn

So A is a zero divisor in Zn.

I feel the first implication is a bit unrigorous.