My Math Forum Wilson's theorem proof

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 July 15th, 2009, 07:40 AM #1 Newbie   Joined: Jul 2009 Posts: 2 Thanks: 0 Wilson's theorem proof Hello! My question is simple: What do you think my own Wilson's theorem proof? http://benmartin.winportal.net/wilson.pdf Is that mathematically correct or isn't it? Thank you Ben
 July 15th, 2009, 12:01 PM #2 Senior Member   Joined: Nov 2007 Posts: 258 Thanks: 0 Re: Wilson's theorem proof I'm not sure about that last step. In any case there are much simpler proofs. Here is mine : Take $\alpha$ to be a primitive root mod $p$; then $(p-1)!= \alpha \times \alpha^2 \times ... \times \alpha^{p-1} = \alpha^{1+...+p-1}=\alpha^{p(p-1)/2} \equiv \alpha^{(p-1)/2}=\left ( \frac{\alpha}{p}\right ) = -1$ since a primitive root is not a quadratic residue.

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### wilson's theorem proof pdf

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