Solutions of Pell's equation \(v^2- (ka^2+ b^2)w^2= -k\) by the ideals of the quadratic fields \(\mathbb{Q} (\sqrt{ka^2+ b^2})\)

DOI10.1016/S0723-0869(01)80004-9zbMath0982.11012MaRDI QIDQ5947330

Lionel Bapoungué

Publication date: 8 April 2002

Published in: Expositiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

ordersquadratic Diophantine equationidealscontinued fraction solutionssolutions of Pell's equation

Mathematics Subject Classification ID

Quadratic extensions (11R11) Quadratic and bilinear Diophantine equations (11D09) Continued fractions (11A55)

Related Items (1)

Factorization in a non-maximal order of a quadratic field

Cites Work

• A solvability criterion for the diophantine equation \(ax^2+2bxy-kay^2=\pm 1\)
• On the general solutions of the diophantine equation \(ax^2+ 2bxy- kay^2= \pm 1\)
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Solutions of Pell's equation \(v^2- (ka^2+ b^2)w^2= -k\) by the ideals of the quadratic fields \(\mathbb{Q} (\sqrt{ka^2+ b^2})\)