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f(f(x) + y) = f(x) + 3x + yf(y) , for x,y>0, f: (0,+\infty)\to(0,+\infty),

Source: Balkan BMO Shortlist 2016 A6

July 30, 2019
functional equationfunctionalgebraIMO Shortlist

Problem Statement

Prove that there is no function from positive real numbers to itself, f:(0,+∞)→(0,+∞)f : (0,+\infty)\to(0,+\infty) such that: f(f(x)+y)=f(x)+3x+yf(y)f(f(x) + y) = f(x) + 3x + yf(y) ,for every x,y∈(0,+∞)x,y \in (0,+\infty)
by Greece, Athanasios Kontogeorgis (aka socrates)
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