### International Mathematics Competition for University Students

July 22 – 28 2018, Blagoevgrad, Bulgaria

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Problem 10. For $\displaystyle R>1$ let $\displaystyle \mathcal{D}_R = \{(a,b)\in\mathbb{Z}^2 \colon 0<a^2+b^2<R\}$. Compute
$\displaystyle \lim_{R\rightarrow \infty} \sum_{(a,b) \in \mathcal{D}_R} \frac{(-1)^{a+b}}{a^2+b^2}.$