MathDB

binomial coeffcient and relation divisible

Source: 11-th Hungary-Israel Binational Mathematical Competition 2000

April 20, 2007

algebrabinomial theoremnumber theory unsolvednumber theory

Problem Statement

Prove or disprove: For any positive integer

k

there exists an integer

n > 1

such that the binomial coeffcient

\binom{n}{i}

is divisible by

k

for any

1 \leq i \leq n-1.