The automorphism of the cyclic group Z/nZ is , which is of order (link)
, thus Aut(C9) is not isomorphic to C(8).
, when gcd(m,n)=1.
, so the order of Aut(C24) should be 8.
A cyclic group is an abelian group by definition.
, when gcd(m,n)=1. Thus
Note: Someone might give you a more thorough answer for this. This is my attempt to this problem.