Only finitely many Tribonacci Diophantine triples exist-Reference-Cited by-同舟云学术

Only finitely many Tribonacci Diophantine triples exist

Published:2017-07-14 Issue:4 Volume:67 Page:853-862
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Fuchs Clemens¹,Hutle Christoph¹,Irmak Nurettin²,Luca Florian³,Szalay László⁴

Affiliation:

1. University of Salzburg Hellbrunner Str. 34/I 5020 Salzburg Austria

2. Ömer Halisdemir University Nigde Turkey

3. University of Witwatersrand Braamfontein 2000 Johannesburg South Africa

4. University of Sopron Bajcsy-Zsilinszky u. 4. 9400 Sopron Hungary

Abstract

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 < w such that uv + 1, uw + 1, vw + 1 are Tribonacci numbers. The proof depends on the Subspace theorem.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0015/pdf

Reference16 articles.

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