- #1

obo

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## Homework Statement

prove that if p is a prime number that p|B(p,m) where B(p,m) is the ordinary binomial coefficient (i.e. p Choose m) for 0 < m < p

## Homework Equations

B(p,m) = p!/m!(p-m)!

## The Attempt at a Solution

If you factor p out of the binomial coefficient, you're left with (p-1)!/m!(p-m)!, which must be an integer. Thus I need to be able to show that m!(p-m)!|(p-1)! somehow. I've monkeyed around with the expressions to try and recover a multiple of a binomial coefficient or something, but haven't been able to... but I'm getting the feeling that I'm taking the wrong approach here =/

Any hints here would be very much appreciated!

Cheers