An exponential Diophantine equation involving the sum or difference of powers of two Pell numbers

Abstract Let P k and Q k be the k-th terms of the Pell and Pell-Lucas sequences respectively. In this paper, we find all the solutions of the Diophantine equations P n + 1 x ± P n − 1 x = Q m $$\begin{array}\displaystyleP_{n+1}^x\pm P_{n-1}^x=Q_m\end{array}$$ in nonnegative integer variables (m, n, x).