2006 OIM Problems/Problem 6

Problem

Let $n > 1$ be an odd integer. Let $P_0$ and $P_1$ be two consecutive vertices of a regular polygon with $n$ sides. For each $k \ge 2$, define $P_k$ as the vertex of the given polygon which is located in the bisector of $P_{k-1}$ and $P_{k-2}$. Find for what values of $n$ the sequence $P_0, P_1, P_2,\cdots$, runs through all the vertices of the polygon.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions