English

Pell and Pell-Lucas numbers as difference of two repdigits

Number Theory 2023-10-13 v1

Abstract

Let {Pn}n0 \{P_{n}\}_{n\geq 0} be the sequence of Pell numbers defined by P0=0 P_0=0 , P1=1 P_1 =1 and Pn+2=2Pn+1+Pn P_{n+2}= 2P_{n+1} +P_n for all n0 n\geq 0 and let {Qn}n0 \{Q_{n}\}_{n\geq 0} be its companion sequence, the Pell-Lucas numbers defined by Q0=Q1=2 Q_0=Q_1 =2 and Qn+2=2Qn+1+Qn Q_{n+2}= 2Q_{n+1} +Q_n for all n0 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 P6=70=777andQ7=478=55577.P_6=70= 77-7 \quad\quad \hbox{and} \quad\quad Q_7 = 478=555-77.

Cite

@article{arxiv.2310.08422,
  title  = {Pell and Pell-Lucas numbers as difference of two repdigits},
  author = {Bilizimbeye Edjeou and Bernadette Faye},
  journal= {arXiv preprint arXiv:2310.08422},
  year   = {2023}
}

Comments

to appear in Afrika Matematika

R2 v1 2026-06-28T12:48:51.120Z