Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 3"
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== Problem == | == Problem == | ||
Let <math>\displaystyle S</math> be the sum of all positive integers <math>\displaystyle n</math> such that <math>\displaystyle n^2+12n-2007</math> is a perfect square. Find the remainder when <math>\displaystyle S</math> is divided by <math>\displaystyle 1000.</math> | Let <math>\displaystyle S</math> be the sum of all positive integers <math>\displaystyle n</math> such that <math>\displaystyle n^2+12n-2007</math> is a perfect square. Find the remainder when <math>\displaystyle S</math> is divided by <math>\displaystyle 1000.</math> | ||
| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ---- | ||
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| + | *[[Mock AIME 2 2006-2007/Problem 2 | Previous Problem]] | ||
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| + | *[[Mock AIME 2 2006-2007/Problem 4 | Next Problem]] | ||
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| + | *[[Mock AIME 2 2006-2007]] | ||
Revision as of 19:46, 22 August 2006
Problem
Let 
be the sum of all positive integers 
such that 
is a perfect square. Find the remainder when is divided by 
Solution
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