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Same equation with different condition

Source: 2023 Israel Olympic Revenge P3

June 15, 2023
olympic revengefunctional equationalgebrafunction

Problem Statement

Find all (weakly) increasing f ⁣:R→Rf\colon \mathbb{R}\to \mathbb{R} for which f(f(x)+y)=f(f(y)+x)f(f(x)+y)=f(f(y)+x) holds for all x,y∈Rx, y\in \mathbb{R}.
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