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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)=1f(1) = 1 and f(x+y)=f(x)+f(y)+2xyf(x + y) = f(x) + f(y) + 2xy for all integers x,yx, y. Determine f(20)f(20).