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I have the following statement (which is false) and I'm trying to understand why, I can't find a concrete example.

If $a$ belongs to $Z_n$ and $a^2 = 1$ then $a=1$ or $a=-1$

Can someone give me a direction?

Guy

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    Try to utilize $x^2 - 1 = (x+1)(x-1)$ to try to derive a counterexample. You want $n|(x+1)(x-1)$ but it does not divide either of those two factors.2012-10-29
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    Try $n = 8$ ${}{}$2012-10-29
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    This doesn't seem to fall under linear algebra _or_ fields.2012-10-29
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    Try picking $a$ before picking $n$.2012-10-29
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    @dinoboy, I'm sorry but didn't understand how should I proceed from there.2012-10-29

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