MathNet 2015-part-05 — 191 problems (EN–VI) Question 60

Given an integer $n \ge 3$ and a permutation $a_1, a_2, \dots, a_n$ of the first $n$ positive integers, show that at least $\sqrt{n}$ distinct residue classes modulo $n$ occur in the list $a_1, a_1 + a_2, \dots, a_1 + a_2 + \dots + a_n$.