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 $n = 2$.