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Consider the set $\mathbb{Z}_+$ of positive integers and set $E = \big\{\{a,b\}: a\neq b\in\mathbb{Z}_+ \text{ and there is } n\in\mathbb{Z}_+: a+b = n^2\big\}$.

Does the graph $G=(\mathbb{Z}_+,E)$ have cliques of arbitrary sizes? If not, what is its chromatic number?

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