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arXiv · 2106.02895

On length of the period of the continued fraction of $n\sqrt{d}$

Filip Gawron·Tomasz Kobos
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Abstract

For a given quadratic irrational $\alpha$, let us denote by $D(\alpha)$ the length of the periodic part of the continued fraction expansion of $\alpha$. We prove that for a positive integer $d$, which is not a perfect square, the sequence $(D(n\sqrt{d}))_{n=1}^{\infty}$ has infinitely many limit points.

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Filip Gawron, Tomasz Kobos. 2021-06-05. On length of the period of the continued fraction of $n\sqrt{d}$. https://arxiv.org/abs/2106.02895

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