Pell and Pell-Lucas numbers as difference of two repdigits

2023/10/12 by Edjeou, Bilizimbeye, Faye, Bernadette
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.08422

Abstract

Let \P_n\_{n≥ 0} be the sequence of Pell numbers defined by P₀=0 , P₁ =1 and P_n+2= 2P_n+1 +P_n for all n≥ 0 and let \Q_n\_{n≥ 0} be its companion sequence, the Pell-Lucas numbers defined by Q₀=Q₁ =2 and Q_n+2= 2Q_n+1 +Q_n for all n≥ 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 P₆=70= 77-7 \hboxand Q₇ = 478=555-77.

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