Ring Homomorphisms from $\mathbb Z_{20} \to \mathbb Z_{30}$
The order of $a$ obviously divides $30$. It must also divide $20$, because $$ 20a=R(20)=R(0)=0 $$
The order of $a$ obviously divides $30$. It must also divide $20$, because $$ 20a=R(20)=R(0)=0 $$