Problem

Source: 2013 Romania JBMO TST 3.4

Tags: number theory, TSTs



Find all integers $n \ge 2$ with the property: there is a permutation $(a_1,a2,..., a_n)$ of the set $\{1, 2,...,n\}$ so that the numbers $a_1 + a_2 +...+ a_k, k = 1, 2,...,n$ have diffferent remainders when divided by $n$