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f(f(x + y)) = f(x + y) + f(x)f(y) + axy

Source: 2023 Grand Duchy of Lithuania, MC p1 (Baltic Way TST)

March 23, 2024
functional equationalgebra

Problem Statement

Given a non-zero real number aa. Find all functions f:R→Rf : R \to R, such that f(f(x+y))=f(x+y)+f(x)f(y)+axyf(f(x + y)) = f(x + y) + f(x)f(y) + axy for all x,y∈Rx, y \in R.
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