I am working on this problem:

For $\displaystyle a,b \in \mathbb{Z}$, let $\displaystyle S_{a,b}=\{n^2+an+b$ | $\displaystyle n\in\mathbb{Z}\}$.

Suppose we have a collection of sets all of the form $\displaystyle S_{a,b}$ for various a,b and these sets are pairwise disjoint. What is the maximum number of sets there can be?

I see that sets $\displaystyle S_{0,0}$ and $\displaystyle S_{0,2}$ are disjoint but I am not sure the maximum number of pairwise disjoint sets.