Abstract: The goal of this paper is to find, in a simple and rigorous way, all powers of three as the difference of two Fibonacci numbers, that is, we study a Diophantine equation in nonnegative integers n, m and p, where is the Fibonacci sequence. The tools used to solve our main result are properties of continued fractions, linear forms in logarithms, and a version of the Baker-Davenport reduction method in Diophantine approximation. |
Keywords and phrases: linear forms in logarithm, Diophantine equations, Fibonacci sequence, Lucas sequence.
Received: January 8, 2021; Revised: January 22, 2021; Accepted: January 25, 2021; Published: February 22, 2021
How to cite this article: Pagdame Tiebekabe and Ismaïla Diouf, Powers of three as difference of two Fibonacci numbers , JP Journal of Algebra, Number Theory and Applications 49(2) (2021), 185-196. DOI: 10.17654/NT049010185
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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