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f(x + yf(x + y)) = y^2 + f(xf(y + 1))

Source: Switzerland - 2016 Swiss MO Final Round p10

January 14, 2023
algebrafunctionalfunctional equation

Problem Statement

Find all functions f:R→Rf : R \to R such that for all x,y∈Rx, y \in R: f(x+yf(x+y))=y2+f(xf(y+1)).f(x + yf(x + y)) = y^2 + f(xf(y + 1)).
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