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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

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.

MSC:

11A55 Continued fractions
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