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R.A. Mollin
Generalized Lagrange criteria for certain quadratic Diophantine equations
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| Published: |
November 8, 2005
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| Keywords: |
Quadratic Diophantine equations, Continued Fractions, Central Norms |
| Subject: |
Primary: 11D09, 11R11, 11A55. Secondary: 11R29 |
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Abstract
We consider the Diophantine equation of the form
x2-Dy2=\pm4, where D is a positive integer that is
not a perfect square, and provide a
generalization of results of Lagrange with elementary proofs
using only basic properties of simple continued fractions. As a
consequence, we achieve a completely general,
simple
criterion for the central norm to be 4
associated with
principal norm 8 in the simple continued
fraction expansion of
\sqrt{D}.
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| Acknowledgements
The author's research is supported by NSERC Canada grant # A8484.
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| Author information
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada
ramollin@math.ucalgary.ca
http://www.math.ucalgary.ca/~ramollin/
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