- #1

- 68

- 0

## Homework Statement

For any integer n>2, show that there are at least two elements in U(n) that satisfy x^2 = 1.

## Homework Equations

None

## The Attempt at a Solution

If the definition of the group U(n) is "the set of all positive integers less than

*n*and relatively prime to

*n*" then the group U(5) has elements {1,2,3,4}. Clearly then, 1^2 = 1. But I can't drum up any way to get any other elements in the group to equal 1 when squared.

The set U(n) is a group under modulo

*n*, but I am pretty weak on modular arithmetic, and am trying to spend the day boning up on it. So for now, I don't understand how to find another element such that x^2 = 1.