English

On solutions of the Diophantine equation $\mathcal{P}_m-L_n=c$

Number Theory 2022-08-12 v1

Abstract

\noindent In this article, we determine all the integers cc having at least two representations as difference between two linear recurrent sequences. This is a variant of the Pillai's equation. This equation is an exponential Diophantine equation. The proof of our main theorem uses lower bounds for linear forms of logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.

Keywords

Cite

@article{arxiv.2208.05752,
  title  = {On solutions of the Diophantine equation $\mathcal{P}_m-L_n=c$},
  author = {Pagdame Tiebekabe and Serge Adonsou and Ismaïla Diouf},
  journal= {arXiv preprint arXiv:2208.05752},
  year   = {2022}
}