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

Source: 2014 Grand Duchy of Lithuania, Mathematical Contest p1 (Baltic Way TST)

October 3, 2020
algebrafunctionalfunctional equation

Problem Statement

Determine all functions f:R→Rf : R \to R such that f(xy+f(x))=xf(y)+f(x)f(xy + f(x)) = xf(y) + f(x) holds for any x,y∈Rx, y \in R.
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