Theorem 2.5: {n/k} consists of d {n'/k'} stars.

This is to say that a composite star can be formed by putting together simple stars.

proof: Label the points of {n/k} with the elements of Zn. If you start at the 0 point and trace out the star, you will run through the cyclic subgroup generated by k. The closest that you get to the 0, point will be the smallest integer which can be expressed in the form sk - tn, where s and t are positive integers, which is well known [7] to be d = GCF(n, k). This number can be found using the Euclidean Algorithm. The points

{d, 2d, . . . , (n/d)d = n = 0}

will constitute n' points equally spaced on a circle, and when you trace out the {n/k} star, you will be connecting every k' of them. In short we will trace out a {n'/k'} star which will be simple since n' and k' are relatively prime.

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