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functional for starters III x^2f(yf(x))= y^2f(x)f(f(x))

Source: Norwegian Mathematical Olympiad 2015 - Abel Competition p1b

September 3, 2019

functionfunctional equationalgebra

Problem Statement

Find all functions

f : R \to R

such that

x^2f(yf(x))= y^2f(x)f(f(x))

for all real numbers

x

and

y