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arXiv · 2207.11331

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

Pagdame Tiebekabe·Serge Adonsou
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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.

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Pagdame Tiebekabe, Serge Adonsou. 2022-07-22. On Pillai's problem involving two linear recurrent sequences : Padovan and Fibonacci. https://doi.org/10.26637/mjm1003%2F003

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