Work

Only finitely many Tribonacci Diophantine triples exist

Year: 2017

Type: article

Abstract: Diophantine triples taking values in recurrence sequences have recently been studied quite a lot. In particular the question was raised whether or not there are finitely many Diophantine triples in the Tribonacci sequence. We answer this question here in the affirmative. We prove that there are only finitely many triples of integers 1 ≤u<v<wsuch thatuv+ 1,uw+ 1,vw+ 1 are Tribonacci numbers. The proof depends on the Subspace theorem.

Source: Mathematica Slovaca

DOI: 10.1515/ms-2017-0015

Authors: Clemens Fuchs, Christoph Hutle, Nurettin Irmak, Florian Luca, László Szalay

Institutions: University of Salzburg, Niğde Ömer Halisdemir Üniversitesi, University of the Witwatersrand, University of Sopron

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Austrian Science Fund

Award: Explicit Problems in Diophantine Analysis and Geometry