Problem

Source: Romania TST 2015 Day 4 Problem 2

Tags: binomial coefficients, Romanian TST, number theory



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