Question 108
Find all integers $n \geqslant 2$ for which there exist a real number $r\gt 0$ and $n$ real numbers $a_{1}\lt a_{2}\lt \cdots\lt a_{n}$ such that the $n(n-1) / 2$ differences $a_{j}-a_{i}$ obtained for $1 \leqslant i\lt j \leqslant n$ are equal, up to order, to the numbers $r^{1}, r^{2}, \ldots, r^{n(n-1) / 2}$.