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ON THE OPTIMAL CONTINUED FRACTION EXPANSION OF A QUADRATIC SURD

Part of: Elementary number theory Computational number theory

Published online by Cambridge University Press:  07 February 2013

KEITH R. MATTHEWS
KEITH R. MATTHEWS*
Affiliation:
Department of Mathematics, University of Queensland, Brisbane 4072, Australia email keithmatt@gmail.com Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia email keithmatt@gmail.com
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Abstract

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We describe the period structure of the optimal continued fraction expansion of a quadratic surd, in terms of the period of its nearest square continued fraction expansion. The analysis results in a faster algorithm for determining the optimal continued fraction expansion of a quadratic surd.

Keywords

optimal continued fractionnearest square continued fractionquadratic surdperiod length

MSC classification

Secondary: 11A55: Continued fractions 11Y65: Continued fraction calculations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 1-2 , October 2012 , pp. 133 - 156
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

References

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