2000 AIME II Problems/Problem 2
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Problem
A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the hyperbola 
?
Solution
We must have 
and 
as both even or else x,y would not be an integer. We first give a factor of two to both and . We have 
left. Since there are 
factors of , and since both x and y can be negative, this gives us 
lattice points.
| 2000 AIME II (Problems • Resources) | ||
| Preceded by Problem 1 | Followed by Problem 3 | |
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