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R. A. Mollin
A Simple Criterion for Solvability of Both X2-DY2= c and x2-Dy2=-c
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| Published: |
September 6, 2001
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| Keywords: |
continued fractions, Diophantine equations, fundamental units, simultaneous solutions |
| Subject: |
11A55, 11R11, 11D09 |
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Abstract
This article provides a simple criterion for the simultaneous
solvability of the Diophantine equations
X2-DY2=c and x2-Dy2=-c when c∈Z, and D∈N is not a perfect square.
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| Acknowledgements
This author's research is supported by NSERC Canada grant # A8484.
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| Author information
Dept. of Math. and Stat., 2500 University Drive, Calgary, Alberta, T2N 1N4, Canada
ramollin@math.ucalgary.ca
http://www.math.ucalgary.ca/~ramollin/
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