Question

Prove that if p is prime and 1 <= k < p

that p divides p!/(k!(p-k)!) (this is the binomial coefficient for C(p,k))

Answer 1

k! and (p-k)! only contain prime factors that are smaller than p, so they can't divide p (because p is prime), the binomial coefficient will thus have to contain a factor p in its prime factorization.

Answer 2

Thanks. I was stumped, but in hindsight, that is surprisingly simple