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anemone

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$Q(a,\,b)=\dfrac{a^2b+2ab^2-5}{ab+1}$.

Let $(a_1,\,b_1),\,(a_2,\,b_2),\,\cdots, (a_n,\,b_n)$ be all pairs of positive integers such that $Q(a,\,b)$ is an integer. Calculate $\displaystyle \sum_{i=1}^n a_i$,