3

Part of 2014 Benelux

Problems(1)

2k-l and 2l-k divide n

Source: Benelux MO 2014 Problem 3

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

2\ell-k

is a (not necessarily positive) divisor of

n

inequalitiesnumber theory unsolvednumber theory