Difference between revisions of "2000 AIME II Problems/Problem 2"

Revision as of 18:22, 11 November 2007

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

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 == Problem ==
-Let <math>u</math> and <math>v</math> be integers satisfying <math>0 < v < u</math>. Let <math>A = (u,v)</math>, let <math>B</math> be the reflection of <math>A</math> across the line <math>y = x</math>, let <math>C</math> be the reflection of <math>B</math> across the y-axis, let <math>D</math> be the reflection of <math>C</math> across the x-axis, and let <math>E</math> be the reflection of <math>D</math> across the y-axis. The area of pentagon <math>ABCDE</math> is <math>451</math>. Find <math>u + v</math>.
+A point whose coordinates are both integers is called a lattice point.  How many lattice points lie on the hyperbola <math>x^2 - y^2 = 2000^2.</math>
 == Solution ==

2000 AIME II (Problems • Answer Key • Resources)
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