Determine all integers such that there exists a permutation of the numbers with the property that the numbers are pairwise distinct modulo .
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
$$x_0, \hspace{0.3cm} x_0 + x_1, \hspace{0.3cm} \ldots, \hspace{0.3cm} x_0 + x_1 + \ldots + x_{n - 1}$$are pairwise distinct modulo $n$.
Source: Srednjoeuropska matematička olimpijada 2017, ekipno natjecanje, problem 7
Školjka 
such that there exists a permutation 
of the numbers 
with the property that the 
numbers 
are pairwise distinct modulo