Question 33
In the plane, where an orthonormal reference system has been taken, all points $(m, n)$ are considered whose coordinates are integers. All the segments that join any of these points and whose length is integer are assumed to be traced. Prove that there are not two of those segments that form an angle of $45^{\circ}$. If the same is done with the points $(m, n, k)$ of the space. Will there be any pair of those segments that form an angle of $45^{\circ}$?