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Criteria for Simultaneous Solutions of X2 − DY2 = c and x2 − Dy2 = −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., website: http://www.math.ucalgary.ca/∼ramollin/ email: ramollin@math.ucalgary.ca
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Abstract

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The purpose of this article is to provide criteria for the simultaneous solvability of the Diophantine equations ${{X}^{2}}-D{{Y}^{2}}\,=\,c$ and ${{x}^{2}}-D{{y}^{2}}=-c$ when $c\,\in \,\mathbb{Z}$, and $D\,\in \,\mathbb{N}$ is not a perfect square. This continues work in [6]–[8].

Keywords

11A5511R1111D09continued fractionsDiophantine equationsfundamental unitssimultaneous solutions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 3 , 01 September 2002 , pp. 428 - 435
Copyright
Copyright © Canadian Mathematical Society 2002

References

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