(a) Find a pair of integers (x,y) such that $15x^2 +y^2 = 2^{2000}$ (b) Does there exist a pair of integers $(x,y)$ such that $15x^2 + y^2 = 2^{2000}$ and $x$ is odd?
Problem
Source: Israel Grosman Memorial Mathematical Olympiad 2001 p6
Tags: Diophantine equation, diophantine, number theory