<abstract xmlns="http://www.w3.org/1999/xhtml"> 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 Gn = AGn-1 - Gn-2 with the initial values G0 = 0, G1 = 1.</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 Gn = AGn-1 - Gn-2 with the initial values G0 = 0, G1 = 1.

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

Department of Mathematics, Art and Science Faculty, Niğde University 51240, Niğde,

Institute of Mathematics, University of West Hungary H-9400 Sopron, Ady E. út. 5,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Reduced diophantine quadruples with the binary recurrence G = AG – G

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...

Reduced diophantine quadruples with the binary recurrence G_n = AG_n–1 – G_n–2

Published Online: Apr 22, 2017

Page range: 23 - 31

Received: Sep 01, 2013

Accepted: Jun 01, 2014

DOI: https://doi.org/10.1515/auom-2015-0022

Keywords
Reduced diophantine quadruples, binary recurrences

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Apr 22, 2017

Page range: 23 - 31

Received: Sep 01, 2013

Accepted: Jun 01, 2014

DOI: https://doi.org/10.1515/auom-2015-0022

KeywordsReduced diophantine quadruples, binary recurrences

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Reduced diophantine quadruples with the binary recurrence G_n = AG_n–1 – G_n–2

Keywords
Reduced diophantine quadruples, binary recurrences