2000 AIME II Problems/Problem 2

Problem

A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the hyperbola $x^2 - y^2 = 2000^2$ ?

$(x-y)(x+y)=2000^2=2^8*5^6$

Since there are $7*9=63$ factors of 2000^2, we have 63 lattice points.

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