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

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October 11, 2010
functioninductionquadraticsalgebradomainalgebra unsolved

Problem Statement

Determine all continuous functions f:Rā†’Rf: \mathbb R \to \mathbb R such that f(x + y)f(x - y) = (f(x)f(y))^2,   \forall(x, y) \in\mathbb{R}^2.
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