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Necessary and Sufficient Conditions for the Central Norm to Equal 2h in the Simple Continued Fraction Expansion of $\sqrt{{{2}^{h}}c}$

Published online by Cambridge University Press:  20 November 2018

R. A. Mollin
R. A. Mollin*
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4 e-mail: [email protected]
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Abstract

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We look at the simple continued fraction expansion of $\sqrt{D}$ for any $D\,=\,{{2}^{h}}c$ where $c\,>\,1$ is odd with a goal of determining necessary and sufficient conditions for the central norm (as determined by the infrastructure of the underlying real quadratic order therein) to be ${{2}^{h}}$. At the end of the paper, we also address the case where $D\,=\,c$ is odd and the central norm of $\sqrt{D}$ is equal to 2.

Keywords

11A5511D0911R11quadratic Diophantine equationssimple continued fractionsnorms of idealsinfrastructure of real quadratic fields
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 1 , 01 March 2005 , pp. 121 - 132
Copyright
Copyright © Canadian Mathematical Society 2005

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