Reduced diophantine quadruples with the binary recurrence Gn = AGn–1 – Gn–2

Murat Alp; Nurettin Irmak; László Szalay

doi:10.1515/auom-2015-0022

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Reduced diophantine quadruples with the binary recurrence Gn = AGn–1 – Gn–2

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 23 (2015): Issue 2 (June 2015)

By: Murat Alp, Nurettin Irmak and László Szalay

Open Access

|Apr 2017

Abstract

Given a positive integer A ≠ 2. In this paper, we show that there do not exist two positive integer pairs {a,b} ≠ {c,d} such that the values of ac+1, ad+1 and bc+1, bd+1 are the terms of the sequence {Gn}_n≥0 which satisfies the recurrence relation G_n = AG_n-1 - G_n-2 with the initial values G₀ = 0, G₁ = 1.

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Articles in this issue

DOI: https://doi.org/10.1515/auom-2015-0022 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 23 - 31

Submitted on: Sep 1, 2013

Accepted on: Jun 1, 2014

Published on: Apr 22, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Reduced diophantine quadruples,

binary recurrences

Related subjects:

Mathematics,

General mathematics

© 2017 Murat Alp, Nurettin Irmak, László Szalay, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 23 (2015): Issue 2 (June 2015)