- #1

silvermane

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## Homework Statement

Suppose R is an integral domain. Suppose c in R has c^2 = 1.

Prove that b must equal either 1 or -1.

Also, in Z/12Z, find an element b not equal to -1 or 1, with b^2 = 1

## The Attempt at a Solution

So for the first part, I'm guessing it would be a good idea to factor (b^2 - 1) and notice that the roots are -1, 1. Is that all I have to show? I'm kinda worrying that I don't have enough here. I think I need to incorporate the fact that this is an integral domain. :/

For the second part (Z/12Z) I know that such an element,7^2 [tex]\equiv[/tex] 49mod12 [tex]\equiv[/tex]1mod12