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2k-l and 2l-k divide n

Source: Benelux MO 2014 Problem 3

July 17, 2014
inequalitiesnumber theory unsolvednumber theory

Problem Statement

For all integers n≥2n\ge 2 with the following property:
[*] for each pair of positive divisors k, ℓ<nk,~\ell <n, at least one of the numbers 2k−ℓ2k-\ell and 2ℓ−k2\ell-k is a (not necessarily positive) divisor of nn as well.
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