 |
|
Criteria for Simultaneous Solutions of $X^2 - DY^2 = c$ and $x^2 - Dy^2 = -c$ |
Canad. Math. Bull. 45(2002), 428-435
Published:2002-09-01
Printed: Sep 2002
Printed: Sep 2002
- R. A. Mollin
Abstract
The purpose of this article is to provide criteria for the
simultaneous solvability of the Diophantine equations $X^2 - DY^2 =
c$ and $x^2 - Dy^2 = -c$ when $c \in \mathbb{Z}$, and $D \in
\mathbb{N}$ is not a perfect square. This continues work in
\cite{me}--\cite{alfnme}.
| Keywords: | continued fractions, Diophantine equations, fundamental units, simultaneous solutions |
| MSC Classifications: |
11A55 - Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 11R11 - Quadratic extensions 11D09 - Quadratic and bilinear equations |