The number of non-trivial ring homomorohism from $Z_{20}$ to$ Z_{44}$

Question

Consider $Z_{20}$ and $Z_{44}$ as ring modulo $20$ and $44$ respectively.Then number of non-trivial ring homomorohism from $Z_{20}$ to $Z_{44}$ is?

Answer 1

The number of ring homomorphism from $Z_m$ to $Z_n$ is $2^{W(n)-W(n/g.c.d(m,n))}$ where $W(n)$ is number of prime divisor of $n$. so number of ring homomorphism is 2..out of 2 1 is trivial homomorphism so 1 is non-trivial homomorphism..