# HW7 (Chapter 13, Problem 5, MA453, Fall 2008, Prof. Walther

## Question

Show that every nonzero element of Zn is a unit or a zero-divisor.

Suppose that a is in Zn. If gcd(a, n) = 1, then we know that a is a unit. Suppose that gcd(a, n) = d > 1. Then a(n/d)= (a/d)n = 0, so a is a zero-divisor.

-Neely Misner