Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2022
- DOI:
- arXiv:
- arXiv:2210.04009
- Bibcode:
- 2022arXiv221004009G
- Keywords:
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- Mathematics - Number Theory;
- 11B39;
- 11D72;
- 11J70
- E-Print:
- First version