Über Pell'sche Gleichungen und Kettenbrüche. (On Pell equations and continued fractions)
type: Item
instance of: scholarly article
title: Über Pell'sche Gleichungen und Kettenbrüche. (On Pell equations and continued fractions)
zbMATH Open document ID: 0631.10008
DOI: 10.1007/BF01200225
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: Für quadratfreies, natürliches \(D\geq 2\) sei \(D^*=D\), falls \(D\not\equiv -1 mod 4\), und \(D^*=2D\) sonst. Dann gibt es genau ein natürliches \(m>1\) mit m \(| D^*\), für welches die ``anti- Pellsche'' Gleichung \(x^ 2-Dy^ 2=m\) lösbar ist. Verf. beweist diesen bekannten Satz erstmals vollständig im Rahmen der Theorie der regelmäßigen Kettenbrüche.
Mathematics Subject Classification ID: 11D04
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 4025505
zbMATH Keywords: quadratic diophantine equation
zbMATH Keywords: Pell equation
zbMATH Keywords: anti-Pellian equation
zbMATH Keywords: regular continued fractions
zbMATH Keywords: length of primitive period
zbMATH Keywords: units
author: Franz Halter-Koch
reviewed by: François Fricker
MaRDI profile type: Publication
cites work: An Artin character and representations of primes by binary quadratic forms. II
cites work: A propos des équations antipelliennes
cites work: Sur le 2-groupe des classes d'idéaux des corps quadratiques.
cites work: Pell's equations \(X^ 2-mY^ 2=-1,-4\) and continued fractions
cites work: Q4402415
cites work: Discriminantal divisors of binary quadratic forms
cites work: Q5828139
full work available at URL: https://doi.org/10.1007/bf01200225
OpenAlex ID: W2911658458
description: scientific article; zbMATH DE number 4025505