# How Many Pairs?

$\large \displaystyle x^2+615=2^y$

Let $$\displaystyle (x_{1},y_{1}),(x_{2},y_{2}),\ldots,(x_{n},y_{n})$$ be the integral solution pairs $$\displaystyle (x,y)$$ to the equation above such that $$\displaystyle x_1<x_2<x_3<\ldots.<x_n$$.

Determine the value of $$\displaystyle \sum\limits_{i=1}^n (-1)^ix_iy_i$$.

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