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find all possible values

Source: Olimpiada Rioplatense 2015-Level 3-Problem 5

July 1, 2016
binomial coefficientsnumber theorygreatest common divisorLucas' Theorem

Problem Statement

For a positive integer number nn we denote d(n)d(n) as the greatest common divisor of the binomial coefficients (n+1n),(n+2n),...,(2nn)\dbinom{n+1}{n} , \dbinom{n+2}{n} ,..., \dbinom{2n}{n}. Find all possible values of d(n)d(n)
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