Theorem 2.2: (Coxeter [4]) {n/k} is a simple star if and only if n and k are relatively prime.

proof: Label the points of the star with the elements of Zn. When you proceed from one point to the next, following the star, to get to the next point, you add (or subtract, depending on whether you are proceeding clockwise or counterclockwise) k to the index of each point using arithmetic modulo n. As a result, if you start at the 0 point, you will trace out the cyclic subgroup in Zn generated by k. It is well known [7] that this subgroup fills up all of Zn if and only if k is relatively prime to n.

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