# Math Help - pairwise disjoint sets of {n^2+an+b | n in Z} with a,b in Z

1. ## pairwise disjoint sets of {n^2+an+b | n in Z} with a,b in Z

I am working on this problem:

For $a,b \in \mathbb{Z}$, let $S_{a,b}=\{n^2+an+b$ | $n\in\mathbb{Z}\}$.
Suppose we have a collection of sets all of the form $S_{a,b}$ for various a,b and these sets are pairwise disjoint. What is the maximum number of sets there can be?

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

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