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Groups and FieldsEasyHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Easy problem

Define φ:Z3→Z9\varphi: \mathbb Z_3 \to \mathbb Z_9 by φ(k)=3k mod 9\varphi(k) = 3k \bmod 9. How many elements of Z9\mathbb Z_9 are in im⁡φ\operatorname{im}\varphi?