The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$
András Bíró, Kostadinka Lapkova · Acta Arithmetica · 2015
We solve unconditionally the class number one problem for the $2$-parameter family of real quadratic fields ${\mathbb Q}(\sqrt{d})$ with square-free discriminant $d=(an)^2+4a$ for positive odd integers $a$ and $n$.