Integers represented by binary recursive sequences
Number Theory
2024-08-12 v1
Abstract
This paper is the continuation of \cite{htl}, where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In case of non-degenerate sequences we give bounds for the highest index for which a term can be 0 and bounds on the growth order of the absolute values of the terms, both only in terms of the two initial values, which is a novel feature. Some of these bounds are best possible apart from a multiplicative constant.
Cite
@article{arxiv.2408.04986,
title = {Integers represented by binary recursive sequences},
author = {L. Hajdu and R. Tijdeman},
journal= {arXiv preprint arXiv:2408.04986},
year = {2024}
}