Vol. 5, No. 3, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 723–899
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
A nonextendable Diophantine quadruple arising from a triple of Lucas numbers

A. M. S. Ramasamy and D. Saraswathy

Vol. 5 (2012), No. 3, 257–271
Abstract

We establish that the only positive integral solutions common to the two Pell’s equations U2 18V 2 = 119 and Z2 29V 2 = 196 are U = 41, V = 10 and Z = 52.

Keywords
Lucas numbers, Diophantine property, recurrence relation, simultaneous Pell's equations, characteristic number, factorization, Jacobi symbol
Mathematical Subject Classification 2010
Primary: 11B39
Secondary: 11D09, 11B37
Milestones
Received: 30 October 2010
Revised: 6 October 2011
Accepted: 18 December 2011
Published: 14 April 2013

Communicated by Filip Saidak
Authors
A. M. S. Ramasamy
Department of Mathematics
Pondicherry University
R.V.Nagar
Kalapet
Pondicherry 605014
India
http://www.pondiuni.edu.in
D. Saraswathy
Department of Mathematics
Pondicherry University
R.V.Nagar
Kalapet
Pondicherry 605014
India