Question

Exercise 3.7.7 In this exercise you will identify Aut(Zn).1.Prove that for any [a]Z,multiplication by [a]defines an automorphism afal Zn>Zn,given byafa]()=ak].2.Prove that a:Z>Aut(Zn)defines an injective homomorphism.3.Prove that any automorphism E Aut(Zn)is determined

by (1),and that (1)must be a generator ofZn.4.Prove that o:Z>Aut(Zn)is an isomorphism.

Fig: 1