On a determination of real quadratic fields of class number one and related continued fraction period length less than 25 (Q1178763)

The authors consider quadratic fields \(\mathbb Q(\sqrt d)\) with class number \(h(d)=1\) related to the period length \(k\) of the continued fraction expansion of \[ (\sigma-1+\sqrt d)/\sigma\text{ with } \sigma=1\text{ if } d\equiv 2,3\pmod 4 \text{ and } \sigma=2 \text{ if } d\equiv 1\pmod 4. \] The authors determine (with one possible exception) all the positive square-free integers \(d\) with \(h(d)=1\) and \(k\leq 24\).