Class number one problem for the real quadratic fields $\mathbb{Q}({\sqrt{m^2+2r}})$

preprint2020arXivOpen access

We investigate the class number one problem for a parametric family of real quadratic fields of the form $\mathbb{Q}( \sqrt{m^2+4r})$ for certain positive integers $m$ and $r$ .

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Class number one problem for the real quadratic fields $\mathbb{Q}({\sqrt{m^2+2r}})$

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Class number one problem for the real quadratic fields Q(m2+2r)\mathbb{Q}({\sqrt{m^2+2r}})Q(m2+2r​)

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Class number one problem for the real quadratic fields $\mathbb{Q}({\sqrt{m^2+2r}})$