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Functional equations

Source: Pan African Mathematics Olympiad p5

August 16, 2024
algebrafunctional equationPAMO 2024

Problem Statement

Let R \mathbb{R} denote the set of real numbers. Find all functions f:R→R f: \mathbb{R} \to \mathbb{R} such that
f(x2)−yf(y)=f(x+y)(f(x)−y) f(x^2) - y f(y) = f(x+y)(f(x) - y)
for all real numbers x x and y y .
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