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Functional equation: sum, difference, difference of squares

Source: Canada Repêchage 2017/3

April 13, 2017
algebrafunctional equationfunctiondifference of squaresspecial factorizations

Problem Statement

Determine all functions f:R→Rf : \mathbb{R} \rightarrow \mathbb{R} that satisfy the following equation for all x,y∈Rx, y \in \mathbb{R}. (x+y)f(x−y)=f(x2−y2).(x+y)f(x-y) = f(x^2-y^2).
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