Small class number fields in the family $\mathbb{Q}(\sqrt{9m^2+4m})$

Nimish Mahapatra, Prem Prakash Pandey, Mahesh Ram

We study the class number one problem for real quadratic fields $\mathbb{Q}(\sqrt{9m^2+4m})$, where $m$ is an odd integer. We show that for $m\equiv 1(\mathrm{mod}3)$ there is only one…