olymmath

CR-MO 2006 Problem 2

    Let nn be a positive integer, and let pp be a prime, such that n>pn>p . Prove that : (np)≡⌊np⌋ (modp).\binom np \equiv \left\lfloor\frac{n}{p}\right\rfloor \ \pmod p.

    Dataset text AI-MO AoPS. Quoted with source.

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