English

On arithmetic progressions of positive integers avoiding $p+F_m$ and $q+L_n$

General Mathematics 2025-06-17 v1

Abstract

In this paper, it is proved that there is an arithmetic progression of positive integers such that each of which is expressible neither as p+Fmp+F_m nor as q+Lnq+L_n, where p,q p,q are primes, Fm F_m denotes the m m -th Fibonacci number and Ln L_n denotes the n n -th Lucas number.

Keywords

Cite

@article{arxiv.2506.12047,
  title  = {On arithmetic progressions of positive integers avoiding $p+F_m$ and $q+L_n$},
  author = {Rui-Jing Wang},
  journal= {arXiv preprint arXiv:2506.12047},
  year   = {2025}
}