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Pell Equations: Non-Principal Lagrange Criteria and Central Norms |
Canad. Math. Bull. 55(2012), 774-782
Published:2011-06-14
Printed: Dec 2012
Printed: Dec 2012
- R. A. Mollin,
- A. Srinivasan,
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 |
| MSC Classifications: |
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 |