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

Canadian mathematical bulletin

关键词: continued fractions;    Diophantine equations;    fundamental units;    simultaneous solutions;   

DOI  :  10.4153/CMB-2002-045-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

The purpose of this article is to provide criteria for thesimultaneous solvability of the Diophantine equations $X^2 - DY^2 =c$ and $x^2 - Dy^2 = -c$ when $c in mathbb{Z}$, and $D inmathbb{N}$ is not a perfect square. This continues work incite{me}--cite{alfnme}.

【 授权许可】

Unknown