On the x-coordinates of Pell equations that are products of two Padovan numbers

Mahadi Ddamulira*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Let (P n) n≥0 be the sequence of Padovan numbers defined by P 0 = 0, P 1 = P 2 = 1, and P n+3 = P n+1 + P n for all n ≥ 0. In this paper, we find all positive square-free integers d ≥ 2 such that the Pell equations x 2 − dy 2 = ℓ, where ℓ ∈ {±1, ±4}, have at least two positive integer solutions (x, y) and (x , y ) such that each of x and x is a product of two Padovan numbers.

Original languageEnglish
Article numberA70
Pages (from-to)1-20
Number of pages20
JournalINTEGERS: Electronic Journal of Combinatorial Number Theory
Volume20
Publication statusPublished - 31 Aug 2020

Keywords

  • Padovan number
  • Pell equation
  • linear form in logarithms
  • Reduction method

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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