Difference between revisions of "Mock AIME 4 2006-2007 Problems/Problem 6"
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For how many positive integers <math>n < 1000</math> does there exist a regular <math>n</math>-sided polygon such that the number of diagonals is a nonzero perfect square? | For how many positive integers <math>n < 1000</math> does there exist a regular <math>n</math>-sided polygon such that the number of diagonals is a nonzero perfect square? | ||
==Solution== | ==Solution== | ||
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| + | The formula for the number of diagonals of a convex n-gon is | ||
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| + | <math>\dfrac{n(n-3)}{2}</math> | ||
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| + | We need to find the number of n such that that is a perfect square. | ||
{{solution}} | {{solution}} | ||
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Revision as of 10:40, 8 October 2007
Problem
For how many positive integers 
does there exist a regular 
-sided polygon such that the number of diagonals is a nonzero perfect square?
Solution
The formula for the number of diagonals of a convex n-gon is
We need to find the number of n such that that is a perfect square.
This problem needs a solution. If you have a solution for it, please help us out by adding it.
