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On the period of the continued fraction expansion of ${\sqrt {2^{2n+1}+1}}$

Yann Bugeaud·Florian Luca
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Abstract

In this paper, we prove that the period of the continued fraction expansion of ${\sqrt {2^{n}+1}}$ tends to infinity when $n$ tends to infinity through odd positive integers.

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Yann Bugeaud, Florian Luca. 2004-01-26. On the period of the continued fraction expansion of ${\sqrt {2^{2n+1}+1}}$. https://arxiv.org/abs/math/0401341

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