Only finitely many Tribonacci Diophantine triples exist
Clemens Fuchs, Christoph Hutle, Nurettin Irmak, Florian Luca, László Szalay · Mathematica Slovaca · 2017
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