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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A numerical investigation into the length of the period of the continued fraction expansion of $ \sqrt{D}$


Author: H. C. Williams
Journal: Math. Comp. 36 (1981), 593-601
MSC: Primary 10A32; Secondary 10-04
MathSciNet review: 606518
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0606518-7
PII: S 0025-5718(1981)0606518-7
Article copyright: © Copyright 1981 American Mathematical Society