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Standard functional equation from R to R

Source: Abelkonkurransen Finale 2024, Problem 2b

March 8, 2024

algebrafunctional equationalgebra proposed

Problem Statement

Find all functions

f:\mathbb{R} \to \mathbb{R}

satisfying

xf(f(x)+y)=f(xy)+x^2

for all

x,y \in \mathbb{R}