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

Mahadi Ddamulira, Florian Luca

Research output: Contribution to journalArticleResearchpeer-review

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 languageEnglish
Pages (from-to)1-24
JournalInternational Journal of Number Theory
Volume16
Early online date9 Apr 2020
DOIs
Publication statusE-pub ahead of print - 9 Apr 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

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