Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers

Ahmed Gaber

Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers

Number Theory 2022-10-11 v1

Authors: Ahmed Gaber

Abstract

We solve the two Diophantine equations $P_k=J_n+J_m$ and $Q_k=J_n+J_m$ where $\left\lbrace P_{k}\right\rbrace_{k\geq0}$ , $\left\lbrace Q_{k}\right\rbrace_{k\geq0}$ and $\left\lbrace J_{k}\right\rbrace_{k\geq0}$ are the sequences of Pell numbers, Pell-Lucas numbers and Jacobsthal numbers, respectively. The main tool is the theory of linear forms in logarithms.

Keywords

pell numbers pell-lucas numbers jacobsthal numbers diophantine equations linear forms in logarithms

Cite

@article{arxiv.2210.04009,
  title  = {Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers},
  author = {Ahmed Gaber},
  journal= {arXiv preprint arXiv:2210.04009},
  year   = {2022}
}

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