**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 Z_{n
}*/{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 Z_{n }* to the set of
simple stars defined by k -> {n/k} maps Z_{n }* onto the
set of simple stars. Since {n/k} = {n/n-k}, this map induces a one to
one correspondence between Z_{n }*/{1, -1} and the set of
simple n pointed stars.