Question 11
An integer $n \ge 3$ is said to be a *polygonal pythagorean number* if there are $n$ positive integers, no two of them equal, which can be placed in the vertices of a regular $n$-gon in such a way that the sum of the squares of the numbers in any two consecutive vertices is a perfect square. For instance, 3 is a polygonal pythagorean number because placing 44, 117 and 240 in the vertices of a triangle, we have $44^2 + 117^2 = 125^2$, $117^2 + 240^2 = 267^2$, and $240^2 + 44^2 = 244^2$. Find all polygonal pythagorean numbers.