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f(a + b) = f(a) + f(b) + f(c) + f(d) in N-{O}, with 2ab = c^2 + d^2

Source: RMM Shortlist 2016 A1

July 4, 2019
functional equationalgebrafunctional equation in N

Problem Statement

Determine all functions ff from the set of non-negative integers to itself such that f(a+b)=f(a)+f(b)+f(c)+f(d)f(a + b) = f(a) + f(b) + f(c) + f(d), whenever a,b,c,da, b, c, d, are non-negative integers satisfying 2ab=c2+d22ab = c^2 + d^2.
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