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

Pagdame Tiebekabe; Serge  Adonsou

doi:10.26637/mjm1003/003

Abstract

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.

Keywords:

Linear forms in logarithm, Diophantine equations, Fibonacci sequence, Padovan sequence, Diophantine equation

Mathematics Subject Classification:

11B39, 11J86, 11D61

Authors Imprint References Funding Related Articles Downloads

Pagdame Tiebekabe Cheikh Anta Diop University, Faculty of Science, Department of Mathematics and Computer science, Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications (LACGAA) Dakar, Senegal.
Serge Adonsou African Institute for Mathematical Sciences (AIMS), South Africa.

Pages: 204-215
Date Published: 01-07-2022
Vol. 10 No. 03 (2022): Malaya Journal of Matematik (MJM)

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