# 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.
Originalsprache englisch 18-37 20 The Fibonacci Quarterly 58 1 Veröffentlicht - 13 Feb 2020

### ASJC Scopus subject areas

• !!Algebra and Number Theory

### Fields of Expertise

• Information, Communication & Computing