MathDB
Very hard FE

Source: Russian TST 2014, Day 11 P3 (Group NG), P4 (Groups A & B)

January 8, 2024
algebrafunctional equation

Problem Statement

Find all functions f:Rā†’Rf : \mathbb{R}\to\mathbb{R} such that f(0)=0f(0) = 0 and for any real numbers x,yx, y the following equality holds f(x2+yf(x))+f(y2+xf(y))=f(x+y)2.f(x^2+yf(x))+f(y^2+xf(y))=f(x+y)^2.
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