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(x+y)(f(x)-f(y))=a(x-y)f(x+y) where a given real

Source: 2020 Czech-Polish-Slovak Match p4

October 8, 2020
algebrafunctional equationfunctional

Problem Statement

Let aa be a given real number. Find all functions f:R→Rf : R \to R such that (x+y)(f(x)−f(y))=a(x−y)f(x+y)(x+y)(f(x)-f(y))=a(x-y)f(x+y) holds for all x,y∈Rx,y \in R.
(Walther Janous, Austria)
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