MathNet 2017-part-04 — 176 problems (EN–VI) Question 130

Fix an integer $n \ge 3$ and let $a_0 = n$. Does there exist a permutation $a_1, a_2, \dots, a_{n-1}$ of the first $n-1$ positive integers such that $\sum_{j=0}^{k-1} a_j$ is divisible by $a_k$ for all indices $k \lt n$?