Farhane, Ahmed On the length of the period of the continued fraction expansion of \(\sqrt{n^ 2 + h}\). (Sur la longueur de la période du développement de \(\sqrt{n^ 2 + h}\) en fraction continue.) (French) Zbl 0780.11006 C. R. Acad. Sci., Paris, Sér. I 316, No. 6, 537-540 (1993). Suppose that \(\ell\) is the length of the continued fraction expansion of \(\sqrt{n^ 2+h}\), where \(n,h\in\mathbb{N}\) and \(n^ 2+h\) is not a square. The author gives an effective optimal lower bound for \(\ell\), which improves previous results of A. Schinzel and S. Louboutin. Reviewer: C.Levesque (Quebec) MSC: 11A55 Continued fractions Keywords:period length; continued fraction expansion; effective optimal lower bound PDFBibTeX XMLCite \textit{A. Farhane}, C. R. Acad. Sci., Paris, Sér. I 316, No. 6, 537--540 (1993; Zbl 0780.11006)