IMO Shortlist 2016 problem N6


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Denote by \mathbb{N} the set of all positive integers. Find all functions f:\mathbb{N}\rightarrow \mathbb{N} such that for all positive integers m and n, the integer f(m)+f(n)-mn is nonzero and divides mf(m)+nf(n).

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf