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Fractions of the period of the continued fraction expansion of quadratic integers

Published online by Cambridge University Press:  17 April 2009

A.J. van der Poorten
A.J. van der Poorten
Affiliation:
School of Mathematics, Physics, Computing and Electronics Macquarie University, NSW 2109, Australia
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Abstract

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The elementary nature and simplicity of the theory of continued fractions is mostly well disguised in the literature. This makes one reluctant to quote sources when making a remark on the subject and seems to necessitate redeveloping the theory ab initio. That had best be done succinctly. That is done here and allows the retrieval of some amusing results on pattern in the period of the continued fraction expansion of quadratic integers.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 1 , August 1991 , pp. 155 - 169
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Kaplan, Pierre and Williams, Kenneth S., ‘Pell's equation X 2 − mY 2 = −1, −4 and continued fractions”, J. Number Theory 23 (1986), 169–182.CrossRefGoogle Scholar
[2]Perron, Oskar, Die Lehre von den Kettenbrüchen, Chelsea reprint of 1929 edition.Google Scholar
[3]Stark, H. M., An introduction to number theory (MIT Press, 1978).Google Scholar
[4]van der Poorten, A. J., ‘An introduction to continued fractions’, in Diophantine Analysis, Editors Loxton, J.H. and van der Poorten, A. J., pp. 99–138 (Cambridge University Press, 1986).CrossRefGoogle Scholar