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Functional Equation From FE Lord Vadym Koval

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 11.4

April 5, 2023
algebrafunctional equation

Problem Statement

Find all functions f:Rā†’Rf : \mathbb{R} \to \mathbb{R}, such that for any real x,yx, y holds the following:
f(x+yf(x+y))=f(y2)+xf(y)+f(x)f(x+yf(x+y)) = f(y^2) + xf(y) + f(x)
Proposed by Vadym Koval
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