Question 71
We call an integer $n \ge 3$ polypythagorean if there are $n$ distinct positive integers that you can put around a circle such that the sum of the squares of each pair of neighbouring numbers is a square. Thus, $3$ is a polypythagorean integer because for example for the triple $(44, 117, 240)$, we have $44^2+117^2 = 125^2$, $117^2 + 240^2 = 267^2$ and $240^2 + 44^2 = 244^2$.
Find all polypythagorean integers.
Find all polypythagorean integers.