Unisequences and nearest integer continued fraction midpoint criteria for Pell’s equation

Matthews, Keith R. (2009) Unisequences and nearest integer continued fraction midpoint criteria for Pell’s equation. Journal of Integer Sequences, 12 6: Article 09.6.7.

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Author Matthews, Keith R.
Title Unisequences and nearest integer continued fraction midpoint criteria for Pell’s equation
Journal name Journal of Integer Sequences   Check publisher's open access policy
ISSN 1530-7638
Publication date 2009
Sub-type Article (original research)
Open Access Status File (Publisher version)
Volume 12
Issue 6
Start page Article 09.6.7
Total pages 24
Editor J.O. Shallit
Place of publication Waterloo, ON, Canada
Publisher University of Waterloo, Department of Computer Science
Collection year 2010
Language eng
Subject 970101 Expanding Knowledge in the Mathematical Sciences
010101 Algebra and Number Theory
Formatted abstract
The nearest integer continued fractions of Hurwitz, Minnegerode (NICF-H) and in Perron’s book Die Lehre von den Kettenbrüchen (NICF-P) are closely related. Mid-point criteria for solving Pell’s equation x2 − Dy2 = ±1 in terms of the NICF-H expansion of √D were derived by H. C. Williams using singular continued fractions. We derive these criteria without the use of singular continued fractions. We use an algorithm for converting the regular continued fraction expansion of √D to its NICF-P expansion.
Keyword Midpoint criteria
Nearest integer continued fraction
Period?length
Unisequence
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
 
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Created: Fri, 06 Nov 2009, 11:34:07 EST by Marie Grove on behalf of School of Mathematics & Physics