MathCastle
Groups and FieldsMediumHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Medium problem

Let φ:Z20→Z8\varphi: \mathbb Z_{20} \to \mathbb Z_8 be given by φ(k)=6k mod 8\varphi(k) = 6k \bmod 8 (this is well defined since 6⋅20≡0(mod8)6 \cdot 20 \equiv 0 \pmod 8). How many elements does ker⁡φ\ker\varphi have?