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(x + y)(f (x)-f (y)) = f (x^2) - f (y^2)

Source: 2004 VMEO I p5 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__vietnam_mathematical

September 26, 2021
algebrafunctional equationfunctional

Problem Statement

Find all the functions f:R→Rf:R \to R satisfying (x+y)(f(x)−f(y))=f(x2)−f(y2), ∀x,y∈R(x + y)(f (x)-f (y)) = f (x^2) - f (y^2),\, \forall x, y \in R
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