(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

None

3. The attempt at a solution

If the definition of the group U(n) is "the set of all positive integers less thannand relatively prime ton" 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 modulon, 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.

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# Abstract Algebra: Question About the Elements in U(n)

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