Thread: prove if p is prime then...

Prove that if p is prime and 1 less than or equal to k less than p then the binomial coefficient p = (p!)/(k!(p-k)!) is divisible by p.
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Originally Posted by mandy123

Prove that if p is prime and 1 less than or equal to k less than p then the binomial coefficient p = (p!)/(k!(p-k)!) is divisible by p.

This proves that for any we have that is divisible by . Now because is a prime this means is divisible by thus is divisibly by .