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IMO 2016 Shortlist, N6

Source:

July 19, 2017
number theoryIMO ShortlistfunctionDivisibility

Problem Statement

Denote by N\mathbb{N} the set of all positive integers. Find all functions f:N→Nf:\mathbb{N}\rightarrow \mathbb{N} such that for all positive integers mm and nn, the integer f(m)+f(n)−mnf(m)+f(n)-mn is nonzero and divides mf(m)+nf(n)mf(m)+nf(n).
Proposed by Dorlir Ahmeti, Albania
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