A nonextendable Diophantine quadruple arising from a triple of Lucas numbers

Ramasamy, A. M. S.; Saraswathy, D.

doi:10.2140/involve.2012.5.257

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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

DOI: 10.2140/involve.2012.5.257

Abstract

We establish that the only positive integral solutions common to the two Pell’s equations $U^{2} - 18 V^{2} = - 119$ and $Z^{2} - 29 V^{2} = - 196$ 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

Vol. 5, No. 3, 2012