The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$
Volume 172 / 2016
Acta Arithmetica 172 (2016), 117-131
MSC: Primary 11R11; Secondary 11R29, 11R42.
DOI: 10.4064/aa7957-12-2015
Published online: 3 December 2015
Abstract
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 $n$.
