Theorem 2.3: If n > 2 then there are E(n)/2 simple n pointed stars. Moreover, there is a one to one correspondence between the simple n pointed stars and the elements of the group Zn */{1, -1}.

proof: It will suffice to verify the last assertion which follows directly from the fact that {n/k} is simple if and only if k is relatively prime to n. The map from Zn * to the set of simple stars defined by k -> {n/k} maps Zn * onto the set of simple stars. Since {n/k} = {n/n-k}, this map induces a one to one correspondence between Zn */{1, -1} and the set of simple n pointed stars.

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