What are the units of Z? In other words find Z^x.

Here is some background:

Every element in a ring has an additive inverse, but only some elements

have multiplicative inverses. Any element with a multiplicative inverse is

called a

unit. Recall that we assume all rings have a multiplicative identity.

Let R be a ring with multiplicative identity 1. If a, b eR are

such that ab = ba = 1 then we say that a and b are multiplicative inverses.

An element a e R is called a unit if it has an inverse. The set of units is

written R:

R^x = {u e R | u is a unit}