OMM 2018 Problem 5

Let $n\geq 5$ an integer and consider a regular $n$ -gon. Initially, Nacho is situated in one of the vertices of the $n$ -gon, in which he puts a flag. He will start moving clockwise. First, he moves one position and puts another flag, then, two positions and puts another flag, etcetera, until he finally moves $n-1$ positions and puts a flag, in such a way that he puts $n$ flags in total. ¿For which values of $n$ , Nacho will have put a flag in each of the $n$ vertices?