On the Diophantine equation \(\sum_{j=1}^kjP_j^p=P_n^q\) (Q2221046)

The Pell numbers are defined recursively as \(P_0 = 0\), \(P_1 = 1\), and \(P_n = 2P_{n-1} + P_{n-2}\) for all \(n \geq 2\). The paper under review finds all solutions of the diophantine equations \( P_1^p+2P_2^p+3P_3^p+\ldots +kP_k^p=P_n^q\) in variables \(k,n\), when \(p,q\in\{1,2\}\).