Question 170
We call an integer $n \ge 3$ polypythagorean if there are $n$ distinct positive numbers that can be placed one after another in a circle such that the sum of the squares of every pair of consecutive numbers is a square. For example, $3$ is a polypythagorean number because with $44$, $117$ and $240$ you have a triple for which $44^2 + 117^2 = 125^2$, $117^2 + 240^2 = 267^2$ and $240^2 + 44^2 = 244^2$.
Find all polypythagorean numbers.
Find all polypythagorean numbers.