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Fermat little theorem

rula

Hi everyone

i need help how to
prove that (2p − 1)! ≡ p (mod p^ 2 ).

Reply 1

Kindred

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 :smile:

You may also be able to google it.

Sorry I can't help myself. Good luck.

Reply 2

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?

Reply 3

DFranklin

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...

Reply 4

Zacken

As above: *coughs* Wil... *coughs*

Reply 5

username1162972

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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