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Problem 6 of Fourth round

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

December 31, 2019
algebrafunctional equation

Problem Statement

Find all functions f:R→Rf: \mathbb{R}\rightarrow \mathbb{R} such that for ∀\forall x,y∈Rx,y\in \mathbb{R} : f(x+f(x+y))+xy=yf(x)+f(x)+f(y)+xf(x+f(x+y))+xy=yf(x)+f(x)+f(y)+x.
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