On a problem of Pillai with k–generalized Fibonacci numbers and powers of 2

Mahadi Ddamulira, Carlos Alexis Gómez Ruiz, Florian Luca

Research output: Contribution to journalArticle

Abstract

For an integer k ≥ 2, let {F n } n≥0 be the k–generalized Fibonacci sequence
which starts with 0, . . . , 0, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all integers c having at least two representations as a difference between a k–generalized Fibonacci number and a power of 2 for any fixed k ≥ 4. This paper extends previous work from Ddamulira et al. (Proc Math Sci 127(3): 411–421, 2017. https://doi.org/10.100/s12044-017-0338-3) for the case k = 2 and Bravo et al. (Bull Korean Math Soc 54(3): 069–1080, 2017. https://doi.org/10.4134/BKMS.b160486) for the case k =3.
Original languageEnglish
Pages (from-to)635-664
JournalMonatshefte für Mathematik
Volume187
Issue number4
Early online date17 Jan 2018
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • Diophantine equations
  • Pillai's problem
  • Generalized Fibonacci sequence
  • Reduction method

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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