Question 5
Find all positive integers $n \geqslant 2$ for which there exist $n$ real numbers $a_{1}\lt \cdots\lt a_{n}$ and a real number $r\gt 0$ such that the $\frac{1}{2} n(n-1)$ differences $a_{j}-a_{i}$ for $1 \leqslant i\lt j \leqslant n$ are equal, in some order, to the numbers $r^{1}, r^{2}, \ldots, r^{\frac{1}{2} n(n-1)}$.