Problem

Source: Benelux MO 2014 Problem 3

Tags: inequalities, number theory unsolved, number theory



For all integers $n\ge 2$ with the following property: for each pair of positive divisors $k,~\ell <n$, at least one of the numbers $2k-\ell$ and $2\ell-k$ is a (not necessarily positive) divisor of $n$ as well.