We solve unconditionally the class number one problem for the 2-parameter family of real quadratic fields ℚ(√d) with square-free discriminant d = (an)²+4a for positive odd integers a and n.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa7957-12-2015,
author = {Andr\'as Bir\'o and Kostadinka Lapkova},
title = {The class number one problem for the real quadratic fields $\mathbb{Q}$($\surd$((an)$^2$+4a))},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {117-131},
zbl = {06545343},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa7957-12-2015}
}
András Biró; Kostadinka Lapkova. The class number one problem for the real quadratic fields ℚ(√((an)²+4a)). Acta Arithmetica, Tome 172 (2016) pp. 117-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa7957-12-2015/