A nonextendable Diophantine quadruple arising from a triple of Lucas numbers

A. M. S. Ramasamy; D. Saraswathy

doi:10.2140/involve.2012.5.257

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Home > Journals > Involve > Volume 5 > Issue 3 > Article

2012 A nonextendable Diophantine quadruple arising from a triple of Lucas numbers

A. M. S. Ramasamy, D. Saraswathy

Involve 5(3): 257-271 (2012). DOI: 10.2140/involve.2012.5.257

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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 $Z = 52$ .

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A. M. S. Ramasamy. D. Saraswathy. "A nonextendable Diophantine quadruple arising from a triple of Lucas numbers." Involve 5 (3) 257 - 271, 2012. https://doi.org/10.2140/involve.2012.5.257

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Received: 30 October 2010; Revised: 6 October 2011; Accepted: 18 December 2011; Published: 2012

First available in Project Euclid: 20 December 2017

zbMATH: 1272.11033

MathSciNet: MR3044612

Digital Object Identifier: 10.2140/involve.2012.5.257

Subjects:

Primary: 11B39

Secondary: 11B37 , 11D09

Keywords: characteristic number , Diophantine property , factorization , Jacobi symbol , Lucas numbers , recurrence relation , simultaneous Pell's equations

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A. M. S. Ramasamy, D. Saraswathy "A nonextendable Diophantine quadruple arising from a triple of Lucas numbers," Involve: A Journal of Mathematics, Involve 5(3), 257-271, (2012)

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