I posted this question but I am not getting anywhere with this question, any help would be very appreciated:(adsbygoogle = window.adsbygoogle || []).push({});

1. let [tex]p[/tex] be odd prime explain why: [tex]2*4*...*(p-1)\equiv (2-p)(4-p)*...*(p-1-p)\equiv(-1)^{(p-1)/2}*1*3*...*(p-2)[/tex] mod [tex]p[/tex].

2. Using number 2 and wilson's thereom [[tex](p-1)!\equiv-1[/tex] mod p] prove [tex]1^23^25^2*....*(p-2)^2\equiv(-1)^{(p-1)/2}[/tex] mod [tex]p[/tex]

Thanks.

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# Number Theory: Wilson's Theorem

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