1. The problem statement, all variables and given/known data 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. 3. 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.