Pell Equations: Non-Principal Lagrange Criteria and Central Norms

Canadian mathematical bulletin

A. Srinivasan¹  R. A. Mollin² 

[1] Department of Mathematics, Siddhartha college, India;Department of Mathematics and Statistics, University of Calgary, Calgary, AB

关键词: Pell's equation;    continued fractions;    central norms;   

DOI  :  10.4153/CMB-2011-118-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 $D$.

【 授权许可】

Unknown