On Pillai's problem involving two linear recurrent sequences: Padovan and Fibonacci

Pagdame Tiebekabe, Serge Adonsou

Published 2022-07-22Version 1

In this paper, we find all integers $c$ having at least two representations as a difference between linear recurrent sequences. This problem is a pillai problem involving Padovan and Fibonacci sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.