Vol. 5, No. 3, 2012

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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 ${U}^{2}-18{V}^{2}=-119$ 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