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I've been asked to attempt a proof of the following congruence. It is found in a section of my textbook with Wilson's theorem and Fermat's Little theorem. I've pondered the problem for a while and nothing interesting has occurred to me.

$1^23^2\cdot\cdot\cdot(p-4)^2(p-2)^2\equiv (-1)^{(p+1)/2} (\text{mod} p)$

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    Start from Wilson's theorem. Half of the terms look right... see what you can do with the other half.2012-06-11
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    Exact duplicates: http://math.stackexchange.com/questions/4827/why-is-the-square-of-all-odds-less-than-an-odd-prime-p-congruent-to-1p http://math.stackexchange.com/questions/22399/if-p-is-an-odd-prime-prove-that-1232-52-p-22-equiv-1p1-2 http://math.stackexchange.com/questions/147438/32-52-ldots-p-22-equiv-1-fracp12-mathrmmod-p2012-06-12

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