Question 64
Find all integers $n \ge 2$ with the following property: every $n$ pairwise distinct integers whose sum is not divisible by $n$ can be rearranged as $a_1, a_2, \dots, a_n$ so that $n$ divides $1 \cdot a_1 + 2 \cdot a_2 + \dots + n \cdot a_n$.