Vol. 5, No. 3, 2012

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ISSN: 1944-4184 (e-only)
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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