Let p is a prime number.
Prove that: $$ (p-1)! +1 \equiv 0 \: \pmod p$$
Could you give me some advice?
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1http://en.wikipedia.org/wiki/Wilson%27s_theorem – kingW3 Dec 29 '14 at 17:21
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Note that you only need "half" of the linked question. – quid Dec 29 '14 at 17:21
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@quid: it's not because 2 people has the same question that it's possibly duplicate !! – idm Dec 29 '14 at 17:27
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@idm what is the difference in that case? (except that this is only asks for one implication as I even said) – quid Dec 29 '14 at 17:28
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@quid, come on man! $n$ and $p$ are totally different. What duplicate are you talking about?) – Jihad Dec 29 '14 at 17:29
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@Jihad: no, they are the same, but anyway ! – idm Dec 29 '14 at 17:30
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1@Jihad come op map they are netty iperchapgable :-) – quid Dec 29 '14 at 17:31
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@idm probably I should add "sarcasm". – Jihad Dec 29 '14 at 17:31
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@idm if you would explain your point a bit more I might see it. – quid Dec 29 '14 at 17:31
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@ quid: I haven't seen that. Thanks anyway – user3000 Dec 29 '14 at 17:46
1 Answers
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Hint: Consider $x^{p-1}-1=0$ over $\mathbb{Z}_p$. What can you say about roots of the equation? (you can use Fermat's little theorem) Then use Vieta's formulas (the last one).
user35603
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