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Yet another (but nice!) functional equation

Source: Brazilian Math Olympiad 2006, Problem 3

October 30, 2006
functioninductionalgebrafunctional equationalgebra unsolved

Problem Statement

Find all functions f ⁣:R→Rf\colon \mathbb{R}\to \mathbb{R} such that f(xf(y)+f(x))=2f(x)+xyf(xf(y)+f(x)) = 2f(x)+xy for every reals x,yx,y.
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