A numerical investigation into the length of the period of the continued fraction expansion of √𝐷

Williams, H. C.

doi:10.1090/S0025-5718-1981-0606518-7

A numerical investigation into the length of the period of the continued fraction expansion of $\sqrt {D}$
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Math. Comp. 36 (1981), 593-601 Request permission

Abstract:

Let $p(D)$ be the length of the period of the continued fraction expansion of $\sqrt D$, where D is a positive square-free integer. In this paper it is suggested that $p(D) = O(\sqrt D \log \log D)$ and several tables of numerical results, which support this suggestion, are provided.

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