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# Fermat little theorem watch

1. Hi everyone

i need help how to
prove that (2p − 1)! ≡ p (mod p^ 2 ).
2. (Original post by rula)
Hi everyone

i need help how to
prove that (2p − 1)! ≡ p (mod p^ 2 ).
Probably best to ask in a maths forum. This is health
You may also be able to google it.

Sorry I can't help myself. Good luck.
3. I can see a way that doesn't involve Fermat's little theorem, and I'd struggle to hint at it without actually doing it.

Anyone else care to pick up the baton?
4. (Original post by ghostwalker)
I can see a way that doesn't involve Fermat's little theorem, and I'd struggle to hint at it without actually doing it.

Anyone else care to pick up the baton?
I think it follows fairly readily from another named theorem that (unlike Fermat) involves factorials...
5. As above: *coughs* Wil... *coughs*
6. (Original post by rula)
Hi everyone

i need help how to
prove that (2p − 1)! ≡ p (mod p^ 2 ).
U put in the health forum, that is half the priblem mate.
Anyway, you should know it aint fermat since the mod isnt prime, (p^2 obviously isnt prime). U need another therem, the one with (p-1)!

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7. Thanks all - my number theory is so rusty, I thought I might have been missing a trick.
8. (Original post by ghostwalker)
Thanks all - my number theory is so rusty, I thought I might have been missing a trick.
Curious to know what your method was, at an appropriate point...
9. (Original post by Zacken)
As above: *coughs* Wil... *coughs*
You take care of that cough, son.

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