MathCastle
Groups and FieldsChallengeHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Challenge problem

Aut⁡(Z30)\operatorname{Aut}(\mathbb Z_{30}) has order φ(30)=8\varphi(30) = 8. How many of its 88 automorphisms φ\varphi satisfy φ∘φ=id⁡\varphi\circ\varphi = \operatorname{id}?