### Another look at real quadratic fields of relative class number 1

The relative class number ${H}_{d}\left(f\right)$ of a real quadratic field K = ℚ (√m) of discriminant d is defined to be the ratio of the class numbers of ${}_{f}$ and ${}_{K}$, where ${}_{K}$ denotes the ring of integers of K and ${}_{f}$ is the order of conductor f given by $\mathbb{Z}+{f}_{K}$. R. Mollin has shown recently that almost all real quadratic fields have relative class number 1 for some conductor. In this paper we give a characterization of real quadratic fields with relative class number 1 through an elementary approach considering the cases when...