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f (f (x + y) - f (x - y)) = xy

Source: 2014 Swedish Mathematical Competition p3

April 30, 2021
algebrafunctional equationfunctional

Problem Statement

Determine all functions f:R→Rf: \mathbb R \to \mathbb R, such that f(f(x+y)−f(x−y))=xy f (f (x + y) - f (x - y)) = xy for all real xx and yy.
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