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

Mahadi Ddamulira*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Let {Ln}n0 be the sequence of Lucas numbers given by L0 = 2, L1 = 1, and Ln+2 = Ln+1 + Ln for all n ≥ 0. In this paper, for an integer d ≥ 2 that is square-free, we show that there is at most one value of the positive integer x participating in the Pell equation x2 − dy2 = ±1, which is a product of two Lucas numbers, with a few exceptions that we completely characterize.

Original languageEnglish
Pages (from-to)18-37
JournalThe Fibonacci Quarterly
Volume58
Issue number1
Publication statusPublished - 1 Feb 2020

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'On the x-coordinates of Pell equations that are products of two Lucas numbers'. Together they form a unique fingerprint.

  • Cite this