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BMO 2021 problem 2

Source: Balkan MO 2021 P2

September 8, 2021
functional equationalgebraBalkan Mathematics Olympiad

Problem Statement

Find all functions f:R+ā†’R+f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}, such that f(x+f(x)+f(y))=2f(x)+yf(x+f(x)+f(y))=2f(x)+y for all positive reals x,yx,y.
Proposed by Athanasios Kontogeorgis, Greece
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