English

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.

Keywords

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}
}