Question 68
Let $n \ge 2$ be an integer. Find all sets of real numbers $(a_1, a_2, \dots, a_n)$ such that $a_1 - 2a_2, a_2 - 2a_3, \dots, a_{n-1} - 2a_n, a_n - 2a_1$ is a permutation of $a_1, a_2, \dots, a_n$. Note that $a_1, a_2, \dots, a_n$ itself is also a permutation of $a_1, a_2, \dots, a_n$.