Mock AIME 4 2006-2007 Problems/Problem 6

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Problem

For how many positive integers $n < 1000$ does there exist a regular $n$-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

$\dfrac{n(n-3)}{2}$

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.



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