PAGMO 2021 Problem 1

There are $n \geq 2$ coins numbered from $1$ to $n$ . These coins are placed around a circle, not necesarily in order.

In each turn, if we are on the coin numbered $i$ , we will jump to the one $i$ places from it, always in a clockwise order, beginning with coin number 1. For an example, see the figure below.

Find all values of $n$ for which there exists an arrangement of the coins in which every coin will be visited.

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