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arXiv · 2210.04009

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

Ahmed Gaber
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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.

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Ahmed Gaber. 2022-10-08. Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers. https://arxiv.org/abs/2210.04009

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