Question 38
A frog jumps around on the grid points in the plane, from one grid point to another. The frog starts at the point $(0,0)$. Then it makes, successively, a jump of one step horizontally, a jump of $2$ steps vertically, a jump of $3$ steps horizontally, a jump of $4$ steps vertically, et cetera. Determine all $n \gt 0$ such that the frog can be back in $(0,0)$ after $n$ jumps.