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The binomial coefficient congruent to [n/p] mod p.

Source: Costarrican Math Olympiad 2006 - Problem 5.

May 20, 2006
floor functionmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

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