Only finitely many Tribonacci Diophantine triples exist
Number Theory
2016-01-21 v2
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 such that are Tribonacci numbers. The proof depends on the Subspace theorem.
Keywords
Cite
@article{arxiv.1508.07760,
title = {Only finitely many Tribonacci Diophantine triples exist},
author = {Clemens Fuchs and Christoph Hutle and Nurettin Irmak and Florian Luca and Laszlo Szalay},
journal= {arXiv preprint arXiv:1508.07760},
year = {2016}
}
Comments
This is a preprint of the Materials accepted for publication in "Mathematica Slovaca"