Difference between revisions of "2000 AIME II Problems/Problem 2"
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== Solution == | == Solution == | ||
| − | + | <math>(x-y)(x+y)=2000^2=2^8*5^6</math> | |
| + | |||
| + | Since there are <math>7*9=63</math> factors of 2000^2, we have 63 lattice points. | ||
== See also == | == See also == | ||
{{AIME box|year=2000|n=II|num-b=1|num-a=3}} | {{AIME box|year=2000|n=II|num-b=1|num-a=3}} | ||
Revision as of 19:53, 3 January 2008
Problem
A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the hyperbola 
?
Solution
Since there are 
factors of 2000^2, we have 63 lattice points.
See also
| 2000 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
