38

Part of 1984 IMO Longlists

Problems(1)

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

Source:

Determine all continuous functions

f: \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.

functioninductionquadraticsalgebradomainalgebra unsolved