期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1975
卷号：72
期号：12
页码：4720-4722
DOI：10.1073/pnas.72.12.4720
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：The sum of all partial quotients in the regular continued fraction expansions of m/n, for 1 [≤] m [≤] n, is shown to be 6{pi}-2n(ln n)2 + O(n log n(log log n)2). This result is applied to the analysis of what is perhaps the oldest non-trivial algorithm for number-theoretic computations.
关键词：continued fractions ; partial quotients ; number theory
