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

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 3 –  quanta Apr 7 '11 at 14:00
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. –  Willie Wong Apr 7 '11 at 14:33
@willie, I have now done so, thanks. –  Cavenaghi Apr 7 '11 at 14:40

But this is just

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

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

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