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Functional inequality on N

Source: European Mathematical Cup 2017 Problem 1

December 27, 2017
functional equationinequalitiesNatural Numbers

Problem Statement

Find all functions f:N→Nf:\mathbb{N}\rightarrow \mathbb{N} such that the inequality f(x)+yf(f(x))≤x(1+f(y))f(x)+yf(f(x))\le x(1+f(y)) holds for all positive integers x,yx, y.
Proposed by Adrian Beker.
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