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

Mahadi Ddamulira

doi:10.33774/coe-2020-27j3q

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

Mahadi Ddamulira^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

Let {L_n}_n≥₀ be the sequence of Lucas numbers given by L₀ = 2, L₁ = 1, and L_n+2 = L_n+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 language	English
Pages (from-to)	18-37
Journal	The Fibonacci Quarterly
Volume	58
Issue number	1
DOIs	https://doi.org/10.33774/coe-2020-27j3q
Publication status	Published - 1 Feb 2020

ASJC Scopus subject areas

Algebra and Number Theory

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https://doi.org/10.33774/coe-2020-27j3qLicence: CC BY-ND 4.0

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

Abstract

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