Question 62
The sequence $a_1, a_2, \dots, a_n$ consists of the numbers $1, 2, \dots, n$ in some order. For which positive integers $n$ is it possible that the $n+1$ numbers $0, a_1, a_1+a_2, a_1+a_2+a_3, \dots, a_1+a_2+\dots+a_n$ all have different remainders when divided by $n+1$?