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Pell Equations: Non-Principal Lagrange Criteria and Central Norms

  Published:2011-06-14
 Printed: Dec 2012
  • R. A. Mollin,
    Department of Mathematics and Statistics, University of Calgary, Calgary, AB
  • A. Srinivasan,
    Department of Mathematics, Siddhartha college, India
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Abstract

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 $x^2-Dy^2=-1$ in terms of congruence conditions modulo $D$.
Keywords: Pell's equation, continued fractions, central norms Pell's equation, continued fractions, central norms
MSC Classifications: 11D09, 11A55, 11R11, 11R29 show english descriptions Quadratic and bilinear equations
Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
Quadratic extensions
Class numbers, class groups, discriminants
11D09 - Quadratic and bilinear equations
11A55 - Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
11R11 - Quadratic extensions
11R29 - Class numbers, class groups, discriminants
 

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