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

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== Solution ==
 
== Solution ==
{{solution}}
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<math>(x-y)(x+y)=2000^2=2^8*5^6</math>
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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 20:53, 3 January 2008

Problem

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

Solution

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

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

See also

2000 AIME II (ProblemsAnswer KeyResources)
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