Question 17
Let $f : \mathbb{Z} \to \mathbb{Z}$ ($\mathbb{Z}$ is the set of integers) be such that $f(1) = 1$, $f(2) = 20$, $f(-4) = -4$ and $f(x+y) = f(x)+f(y)+axy(x+y)+bxy+c(x+y)+4$ for all $x, y \in \mathbb{Z}$, where $a, b$ and $c$ are certain constants.
a. Find a formula for $f(x)$, where $x$ is any integer.
b. If $f(x) \ge mx^2+(5m+1)x+4m$ for all nonnegative integers $x$, find the greatest possible value of $m$.
a. Find a formula for $f(x)$, where $x$ is any integer.
b. If $f(x) \ge mx^2+(5m+1)x+4m$ for all nonnegative integers $x$, find the greatest possible value of $m$.