International Mathematics Competition for University Students

July 22 – 28 2018, Blagoevgrad, Bulgaria

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Day 1
    Problem 1
    Problem 2
    Problem 3
    Problem 4
    Problem 5

Day 2
    Problem 6
    Problem 7
    Problem 8
    Problem 9
    Problem 10

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Problem 10

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

\(\displaystyle \lim_{R\rightarrow \infty} \sum_{(a,b) \in \mathcal{D}_R} \frac{(-1)^{a+b}}{a^2+b^2}.\)

(Proposed by Rodrigo Angelo, Princeton University and Matheus Secco, PUC, Rio de Janeiro)

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