IMO 1970 LL FRA24

Let n and p be two integers such that 2p \leqn. Prove the

IMO 1970 LL FRA24

Origin: FRA

Problem

Let n and p be two integers such that 2p \leqn. Prove the inequality (n −p)! p! \leq n + 1 n−2p . For which values does equality hold?