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Prove that a binomial coefficient is not divisible by p.

Source: Moldova 2008 IMO-BMO Third TST Problem 2

March 30, 2008

number theory proposednumber theory

Problem Statement

Let

p

be a prime number and

k,n

positive integers so that \gcd(p,n)\equal{}1. Prove that

\binom{n\cdot p^k}{p^k}

and

p

are coprime.