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Maximal number of divisors a binomial coefficient has !!!

Source: Romania TST 2015 Day 4 Problem 2

June 4, 2015
binomial coefficientsRomanian TSTnumber theory

Problem Statement

Given an integer k≥2k \geq 2, determine the largest number of divisors the binomial coefficient (nk)\binom{n}{k} may have in the range n−k+1,…,nn-k+1, \ldots, n , as nn runs through the integers greater than or equal to kk.
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