On arithmetic progressions in Lucas sequences
Number Theory
2017-08-08 v2
Abstract
In this paper, we consider arithmetic progressions contained in Lucas sequences of first and second kind. We prove that for almost all sequences, there are only finitely many and their number can be effectively bounded. We also show that there are only a few sequences which contain infinitely many and one can explicitly list both the sequences and the progressions in them. A more precise statement is given for sequences with dominant root.
Cite
@article{arxiv.1703.06722,
title = {On arithmetic progressions in Lucas sequences},
author = {Lajos Hajdu and Márton Szikszai and Volker Ziegler},
journal= {arXiv preprint arXiv:1703.06722},
year = {2017}
}