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

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

Let $ \{L_n\}_{n\ge 0} $ be the sequence of Lucas numbers given by $ L_0=2, ~ L_1=1 $ and $ L_{n+2}=L_{n+1}+L_n $ for all $ n\ge 0 $. In this paper, for an integer $d\geq 2$ which is square-free, we show that there is at most one value of the positive integer $x$ participating in the Pell equation $x^{2}-dy^{2}
=\pm 1$ which is a product of two Lucas numbers, with a few exceptions that we completely characterize.
Originalspracheenglisch
Seiten (von - bis)18-37
Seitenumfang20
FachzeitschriftThe Fibonacci Quarterly
Jahrgang58
Ausgabenummer1
PublikationsstatusVeröffentlicht - 13 Feb 2020

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    ASJC Scopus subject areas

    • !!Algebra and Number Theory

    Fields of Expertise

    • Information, Communication & Computing

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