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 ${\left\{P_k\right\}}_{k\ge 0}$, ${\left\{Q_k\right\}}_{k\ge 0}$ and ${\left\{J_k\right\}}_{k\ge 0}$ are the sequences of Pell numbers, Pell-Lucas numbers and Jacobsthal numbers, respectively. The main tool is the theory of linear forms in logarithms.

First version