CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Criteria for Simultaneous Solutions of $X^2 - DY^2 = c$ and $x^2 - Dy^2 = -c$

  Published:2002-09-01
 Printed: Sep 2002
  • R. A. Mollin
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

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 continued fractions, Diophantine equations, fundamental units, simultaneous solutions
MSC Classifications: 11A55, 11R11, 11D09 show english descriptions Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
Quadratic extensions
Quadratic and bilinear equations
11A55 - Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
11R11 - Quadratic extensions
11D09 - Quadratic and bilinear equations
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/