Distance between point p and origin

Question

How to prove that the distance between the origin and the point $P$ is a natural number, where $P=(n, n+1, n(n+1))$.

Answer 1

The distance is $$\sqrt{n^2+(n+1)^2+(n(n+1))^2}=\sqrt{(n^2+n)^2+2(n^2+n)+1}=\sqrt{(n^2+n+1)^2}=n^2+n+1$$