MathCastle
Groups and FieldsMediumNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Medium problem

For how many values of a∈{0,1,…,9}a \in \{0,1,\ldots,9\} is φ(k)=ak mod 10\varphi(k) = ak \bmod 10 an injective homomorphism Z10→Z10\mathbb Z_{10} \to \mathbb Z_{10}?