End ZpUnitMorphism.

(* Specifications: *)
Lemma Zp_unitmM : {in units_Zp #[a] &, {morph Zp_unitm : u v / u * v}}.
Canonical Zp_unit_morphism := Morphism Zp_unitmM.
Lemma injm_Zp_unitm : 'injm Zp_unitm.
Lemma generator_coprime m : generator <[a]> (a ^+ m) = coprime #[a] m.
Lemma im_Zp_unitm : Zp_unitm @* units_Zp #[a] = Aut <[a]>.
Lemma Zp_unit_isom : isom (units_Zp #[a]) (Aut <[a]>) Zp_unitm.
Lemma Aut_cycle_abelian : abelian (Aut <[a]>).
End CyclicAutomorphism.
Lemma sum_totient_dvd n : \sum_(d < n.+1 | d %| n) totient d = n.
Section FieldMulCyclic.