MathDB

N6

Part of 2016 IMO Shortlist

Problems(1)

IMO 2016 Shortlist, N6

Source:

7/19/2017
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
number theoryIMO ShortlistfunctionDivisibility