Original scientific paper

https://doi.org/10.3336/gm.49.2.05

Diophantine triples and reduced quadruples with the Lucas sequence of recurrence u_n=Au_n-1-u_n-2

Nurettin Irmak orcid.org/0000-0003-0409-4342 ; Mathematics Department, Art and Science Faculty, University of Niğde, 51240 Niğde, Turkey
László Szalay ; Institute of Mathematics, University of West Hungary, H-9400 Sopron, Hungary

Abstract

In this study, we show that there is no positive integer triple {a, b, c} such that all of ab+1, ac+1 and bc+1 are in the sequence {un}n≥ 0 satisfies the recurrence un=Aun-1-un-2 with the initial values u0=0, u1=1. Further, we investigate the analogous question for the quadruples {a,b,c,d} with abc+1=ux, bcd+1=uy, cda+1=uz and dab+1=ut, and deduce the non-existence of such quadruples.

Keywords

Diophantine triples; Diophantine quadruples; binary recurrence

Hrčak ID:

130885

URI

https://hrcak.srce.hr/130885

Publication date:

18.12.2014.

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