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f(x)+ f(y) = f(x+2xy)+ f(y-2xy), f(-1) = f(1)

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1993 p5

February 20, 2020
functional equationfunctionalalgebra

Problem Statement

Find all functions f:Z→Zf : Z \to Z such that f(−1)=f(1)f(-1) = f(1) and f(x)+f(y)=f(x+2xy)+f(y−2xy)f(x)+ f(y) = f(x+2xy)+ f(y-2xy) for all x,y∈Zx,y \in Z
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