MathCastle
OlympiadSuperchallengeOlympiad Number Theory

Olympiad Number Theory · Superchallenge problem

A function f:Z→Zf : \mathbb{Z} \to \mathbb{Z} satisfies f(1)=2f(1) = 2 and f(x+y)=f(x)+f(y)+6xyf(x + y) = f(x) + f(y) + 6xy for all integers x,yx, y. Determine f(18)f(18).