Question 182
Find all positive integers $n \ge 2$ for which there exist $n$ real numbers
$$
a_1 \lt a_2 \lt \dots \lt a_n
$$
and a real number $r \gt 0$ such that the $\frac{n(n-1)}{2}$ differences $a_j - a_i$ for $1 \le i \lt j \le n$ are equal, in some order, to the numbers
$$
r^1, r^2, \dots, r^{\frac{n(n-1)}{2}}.
$$
$$
a_1 \lt a_2 \lt \dots \lt a_n
$$
and a real number $r \gt 0$ such that the $\frac{n(n-1)}{2}$ differences $a_j - a_i$ for $1 \le i \lt j \le n$ are equal, in some order, to the numbers
$$
r^1, r^2, \dots, r^{\frac{n(n-1)}{2}}.
$$