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Prove $(n -1) = (n-1)^{n}$ mod n

How would one go about doing this?

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    What if n = 4? 3^4 = 1 not 32011-04-07
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    why not just accept TonyK's answer? It is a valid/useful answer for the question as stated. Because other users have contributed content, I'm reluctant to delete the question.2011-04-07
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    @willie, I have now done so, thanks.2011-04-07

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But this is just

$-1 = (-1)^n \mod n$

which is true if and only if $n$ is odd or $n = 2$.