- #1

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- 4

## 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

In my book I found a definition: Define U(n) to be the set of all positive integers less than n and relatively prime to n.

## The Attempt at a Solution

I think I simply just don't understand exactly what is being asked. My first instinct is to just look at an integer greater than 2, say 3. Now I think, "What are some numbers in the set U(3)?" Well, I can only think of 1 and 2, since both 1 and 2 are positive numbers and co-prime to 3. Clearly 1 is a solution, but certainly not 2. Any other number greater than 3 yields the same conclusion, i.e. 1 as the only answer.