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C(n,k) is divisible by n, prime cirterion

Source: Polish MO Finals 1970 p3

August 22, 2024
number theorybinomial coefficientsdivisibleprime

Problem Statement

Prove that an integer n>1n > 1 is a prime number if and only if, for every integer kk with 1≤k≤n−11\le k \le n-1, the binomial coefficient (nk)n \choose k is divisible by nn.
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