On fundamental solutions of binary quadratic form equations

Matthews, Keith R., Robertson, John P. and Srinivasan, Anitha (2015) On fundamental solutions of binary quadratic form equations. Acta Arithmetica, 169 3: 291-299. doi:10.4064/aa169-3-4

Attached Files (Some files may be inaccessible until you login with your UQ eSpace credentials)
Name Description MIMEType Size Downloads

Author Matthews, Keith R.
Robertson, John P.
Srinivasan, Anitha
Title On fundamental solutions of binary quadratic form equations
Journal name Acta Arithmetica   Check publisher's open access policy
ISSN 0065-1036
Publication date 2015-01-01
Sub-type Article (original research)
DOI 10.4064/aa169-3-4
Open Access Status Not Open Access
Volume 169
Issue 3
Start page 291
End page 299
Total pages 9
Place of publication Warsaw, Poland
Publisher Polska Akademia Nauk * Instytut Matematyczny / Polish Academy of Sciences, Institute of Mathematics
Collection year 2016
Language eng
Formatted abstract
We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au2+Buv+Cv2=N, where A>0, N≠0 and B2−4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u2−dv2=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.
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
Official 2016 Collection
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 0 times in Thomson Reuters Web of Science Article
Scopus Citation Count Cited 0 times in Scopus Article
Google Scholar Search Google Scholar
Created: Wed, 24 Jun 2015, 13:56:21 EST by Kay Mackie on behalf of School of Mathematics & Physics