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OlympiadSuperchallengeOlympiad Number Theory

Olympiad Number Theory · Superchallenge problem

A function f:Z→Zf : \mathbb{Z} \to \mathbb{Z} satisfies f(1)=3f(1) = 3 and f(x+y)=f(x)+f(y)+4xyf(x + y) = f(x) + f(y) + 4xy for all integers x,yx, y. Determine f(15)f(15).