MathDB

Consider a regular

n

-gon with

n

odd. Given two adjacent vertices

A_{1}

and

A_{2},

define the sequence

(A_{k})

of vertices of the

n

-gon as follows: For

k\ge 3,\, A_{k}

is the vertex lying on the perpendicular bisector of

A_{k-2}A_{k-1}.

Find all

n

for which each vertex of the

n

-gon occurs in this sequence.

Problem Statement