How Many Pairs?
Number Theory
Level
5
\[ \large \displaystyle x^2+615=2^y\]
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 \(\displaystyle \sum\limits_{i=1}^n (-1)^ix_iy_i\).
by
Satvik Golechha