1. ## Factorial proof

Hi all
I've got a feeling this is a really simple question but I can't see it.

Explain why p divides (2p-1)!

Thanks, Alex

2. ## Re: Factorial proof

Originally Posted by alexlbrown59
Hi all
I've got a feeling this is a really simple question but I can't see it.

Explain why p divides (2p-1)!

Thanks, Alex
$(2p-1)! = (2p-1)(2p-2)\dots (p+1)(p)(p-1)\dots (2)$

$2p-1>p,~\forall p>1$

so $p$ will appear as a product term in this factorial for $p>1$

$1$ divides everything so it works for $p=1$ as well