Is there a nice expression for the number of points in $\mathbb{Z}^3$ which lie a distance of $\sqrt{n}$ from the origin? Here, $n$ is of course a positive integer.
Is there a nice expression for the number of points in $\mathbb{Z}^3$ which lie at precisely a distance of $\sqrt{n}$ from the origin? Here, $n$ is of course a positive integer.