Question 165
Determine all integers $n \geqslant 2$ such that there exists a permutation $x_{0}, x_{1}, \ldots, x_{n-1}$ of the numbers $0,1, \ldots, n-1$ with the property that the $n$ numbers
$$
x_{0}, \quad x_{0}+x_{1}, \quad \ldots, \quad x_{0}+x_{1}+\ldots+x_{n-1}
$$
are pairwise distinct modulo $n$.
$$
x_{0}, \quad x_{0}+x_{1}, \quad \ldots, \quad x_{0}+x_{1}+\ldots+x_{n-1}
$$
are pairwise distinct modulo $n$.