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Groups and FieldsMediumHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Medium problem

Let φ:Z24→Z24\varphi: \mathbb Z_{24} \to \mathbb Z_{24} be φ(k)=9k mod 24\varphi(k) = 9k \bmod 24. How many elements of Z24\mathbb Z_{24} are NOT in im⁡φ\operatorname{im}\varphi?