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Pell Equations: Non-Principal Lagrange Criteria and Central Norms

Published online by Cambridge University Press:  20 November 2018

R. A. Mollin  and
A. Srinivasan
R. A. Mollin
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, ABURL: http://www.math.ucalgary.ca/~ramollin/e-mail: ramollin@math.ucalgary.ca
A. Srinivasan
Affiliation:
Department of Mathematics, Siddhartha college, (affiliated with Mumbai University), Indiae-mail: rsrinivasan.anitha@gmail.com
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Abstract

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We provide a criterion for the central norm to be any value in the simple continued fraction expansion of $\sqrt{D}$ for any non-square integer $D\,>\,1$. We also provide a simple criterion for the solvability of the Pell equation ${{x}^{2}}\,-\,D{{y}^{2}}\,=\,-1$ in terms of congruence conditions modulo $D$.

Keywords

11D0911A5511R1111R29Pell's equationcontinued fractionscentral norms
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 774 - 782
Copyright
Copyright © Canadian Mathematical Society 2012

References

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