# Integral Divisibility

Given that $$a$$ and $$b$$ are positive integers with $$(a_1,b_1), (a_2,b_2),\ldots,(a_n,b_n)$$ as solutions such that $$\dfrac{a^2+b}{b^2-a}$$ and $$\dfrac{b^2+a}{a^2-b}$$ are both integers, find $\sum_{i=1}^{n} a_i b_i.$

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