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

Mahadi Ddamulira; Florian Luca

doi:10.1007/s12044-020-00578-4

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

Mahadi Ddamulira^*, Florian Luca

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

Let {Fn}n≥0 be the sequence of Fibonacci numbers defined by F= 0 , F₁= 1 and F_n₊₂= F_n₊₁+ F_n 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.

Originalsprache	englisch
Aufsatznummer	58
Seitenumfang	21
Fachzeitschrift	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Jahrgang	130
Ausgabenummer	1
Frühes Online-Datum	23 Sept. 2020
DOIs	https://doi.org/10.1007/s12044-020-00578-4
Publikationsstatus	Veröffentlicht - 1 Dez. 2020

ASJC Scopus subject areas

Allgemeine Mathematik

Fields of Expertise

Information, Communication & Computing

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10.1007/s12044-020-00578-4

https://www.ias.ac.in/article/fulltext/pmsc/130/0058Lizenz: CC BY-NC-ND 4.0

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KW - reduction method

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

Abstract

ASJC Scopus subject areas

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