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Groups and FieldsEasyHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Easy problem

For how many elements kk in Z5\mathbb Z_5 is the map φk:Z5→Z5\varphi_k: \mathbb Z_5 \to \mathbb Z_5 given by φk(x)=kx mod 5\varphi_k(x) = kx \bmod 5 an isomorphism?