$k$-Pell-Lucas numbers which are concatenations of two repdigits

Bibhu Prasad Tripathy; Bijan Kumar Patel

$k$-Pell-Lucas numbers which are concatenations of two repdigits

Number Theory 2023-03-10 v1

Authors: Bibhu Prasad Tripathy , Bijan Kumar Patel

Abstract

For any integer $k \geq 2$ , let $\{Q_{n}^{(k)} \}_{n \geq -(k-2)}$ denote the $k$ -generalized Pell-Lucas sequence which starts with $0, \dots ,2,2$ ( $k$ terms) where each next term is the sum of the $k$ preceding terms. In this paper, we find all the $k$ -generalized Pell-Lucas numbers that are concatenations of two repdigits.

Keywords

k-Pell-Lucas numbers repdigits concatenation diophantine equation linear forms in logarithms

Cite

@article{arxiv.2303.05293,
  title  = {$k$-Pell-Lucas numbers which are concatenations of two repdigits},
  author = {Bibhu Prasad Tripathy and Bijan Kumar Patel},
  journal= {arXiv preprint arXiv:2303.05293},
  year   = {2023}
}

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