On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3

Mahadi Ddamulira; Florian Luca

doi:10.1142/S1793042120500876

On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3

Mahadi Ddamulira^*, Florian Luca

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article

Abstract

For an integer k ≥ 2, let {Fn(k)} n≥2-k be the k-generalized Fibonacci sequence which starts with 0,..., 0, 1 (a total of k terms) and for which each term afterwards is the sum of the k preceding terms. In this paper, we find all integers c with at least two representations as a difference between a k-generalized Fibonacci number and a power of 3. This paper continues the previous work of the first author for the Fibonacci numbers, and for the Tribonacci numbers.

Original language	English
Pages (from-to)	1643-1666
Number of pages	24
Journal	International Journal of Number Theory
Volume	16
Issue number	7
DOIs	https://doi.org/10.1142/S1793042120500876
Publication status	Published - 1 Aug 2020

Keywords

Baker's method
generalized Fibonacci numbers
linear forms in logarithms
Pillai's problem

ASJC Scopus subject areas

Algebra and Number Theory

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1142/S1793042120500876Licence: CC BY

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abstract = "For an integer k ≥ 2, let {Fn(k)} n≥2-k be the k-generalized Fibonacci sequence which starts with 0,..., 0, 1 (a total of k terms) and for which each term afterwards is the sum of the k preceding terms. In this paper, we find all integers c with at least two representations as a difference between a k-generalized Fibonacci number and a power of 3. This paper continues the previous work of the first author for the Fibonacci numbers, and for the Tribonacci numbers.",

keywords = "Baker's method, generalized Fibonacci numbers, linear forms in logarithms, Pillai's problem",

author = "Mahadi Ddamulira and Florian Luca",

note = "Mahadi Ddamulira, Florian Luca. On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3. International Journal of Number Theory, World Scientific Publishing, https://doi.org/10.1142/S1793042120500876.",

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