The x-coordinates of Pell equations and sums of two Fibonacci numbers II

Mahadi Ddamulira*, Florian Luca

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let {Fn}n≥0 be the sequence of Fibonacci numbers defined by F= 0 , F1= 1 and Fn+2= Fn+1+ Fn for all n≥ 0. In this paper, for an integer d≥ 2 which is square-free, we show that there is at most one value of the positive integer x participating in the Pell equation x2- dy2= ± 4 which is a sum of two Fibonacci numbers, with a few exceptions that we completely characterize.

Original languageEnglish
Article number58
Number of pages21
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume130
Issue number1
Early online date23 Sep 2020
DOIs
Publication statusPublished - 1 Dec 2020

Keywords

  • Fibonacci number
  • linear form in logarithm
  • Pell equation
  • reduction method

ASJC Scopus subject areas

  • Mathematics(all)

Fields of Expertise

  • Information, Communication & Computing

Fingerprint

Dive into the research topics of 'The x-coordinates of Pell equations and sums of two Fibonacci numbers II'. Together they form a unique fingerprint.

Cite this