Markoff-Rosenberger triples and generalized Lucas sequences
Number Theory
2020-05-29 v1
Abstract
We consider the Markoff-Rosenberger equation with where denotes the -th generalized Lucas number of first/second kind. We provide upper bound for the minimum of the indices and we apply the result to completely resolve concrete equations, e.g. we determine solutions containing only balancing numbers and Jacobsthal numbers, respectively.
Cite
@article{arxiv.2005.13935,
title = {Markoff-Rosenberger triples and generalized Lucas sequences},
author = {Hayder Hashim and László Szalay and Szabolcs Tengely},
journal= {arXiv preprint arXiv:2005.13935},
year = {2020}
}