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Groups and FieldsEasyHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Easy problem

Let φ:Z18→Z18\varphi: \mathbb Z_{18} \to \mathbb Z_{18} be φ(k)=4k mod 18\varphi(k) = 4k \bmod 18. How many elements does im⁡φ\operatorname{im}\varphi have?