Pell and Pell-Lucas numbers as difference of two repdigits

Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Pell numbers defined by $ P_0=0 $, $ P_1 =1$ and $ P_{n+2}= 2P_{n+1} +P_n$ for all $ n\geq 0 $ and let $ \{Q_{n}\}_{n\geq 0} $ be its companion sequence, the Pell-Lucas numbers defined by $ Q_0=Q_1 =2$ and $ Q_{n+2}= 2Q_{n+1} +Q_n$ for a...

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Bibliographic Details
Published in	arXiv.org
Main Authors	Edjeou, Bilizimbeye, Faye, Bernadette
Format	Paper
Language	English
Published	Ithaca Cornell University Library, arXiv.org 12.10.2023
Online Access	Get full text

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Summary:	Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Pell numbers defined by $ P_0=0 $, $ P_1 =1$ and $ P_{n+2}= 2P_{n+1} +P_n$ for all $ n\geq 0 $ and let $ \{Q_{n}\}_{n\geq 0} $ be its companion sequence, the Pell-Lucas numbers defined by $ Q_0=Q_1 =2$ and $ Q_{n+2}= 2Q_{n+1} +Q_n$ for all $ n\geq 0 $ . In this paper, we find all Pell and Pell-Lucas numbers which can be written as difference of two repdigits. It is shown that the largest Pell and Pell-Lucas numbers which can be written as difference of two repdigits are $$P_6=70= 77-7 \quad\quad \hbox{and} \quad\quad Q_7 = 478=555-77.$$
ISSN:	2331-8422

Summary:	Let \( \{P_{n}\}_{n\geq 0} \) be the sequence of Pell numbers defined by \( P_0=0 \), \( P_1 =1\) and \( P_{n+2}= 2P_{n+1} +P_n\) for all \( n\geq 0 \) and let \( \{Q_{n}\}_{n\geq 0} \) be its companion sequence, the Pell-Lucas numbers defined by \( Q_0=Q_1 =2\) and \( Q_{n+2}= 2Q_{n+1} +Q_n\) for all \( n\geq 0 \) . In this paper, we find all Pell and Pell-Lucas numbers which can be written as difference of two repdigits. It is shown that the largest Pell and Pell-Lucas numbers which can be written as difference of two repdigits are $$P_6=70= 77-7 \quad\quad \hbox{and} \quad\quad Q_7 = 478=555-77.$$
ISSN:	2331-8422