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

Source: Nordic Mathematical Contest 2014 #1

September 23, 2017

functional equationfunctionalgebra

Problem Statement

Find all functions

{ f : N \rightarrow N}

(where

{N}

is the set of the natural numbers and is assumed to contain

{0}

), such that

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

for all

{x, y \in N}

with

{x \ge y}