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arXiv · 2310.08422

Pell and Pell-Lucas numbers as difference of two repdigits

Bilizimbeye Edjeou·Bernadette Faye
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Abstract

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 $$P_6=70= 77-7 \quad\quad \hbox{and} \quad\quad Q_7 = 478=555-77.$$

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Bilizimbeye Edjeou, Bernadette Faye. 2023-10-12. Pell and Pell-Lucas numbers as difference of two repdigits. https://arxiv.org/abs/2310.08422

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