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A functional equation from MEMO

Source: Middle European Mathematical Olympiad 2022, problem I-1

September 1, 2022

Problem Statement

Find all functions f:Rā†’Rf: \mathbb R \to \mathbb R such that f(x+f(x+y))=x+f(f(x)+y)f(x+f(x+y))=x+f(f(x)+y) holds for all real numbers xx and yy.
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