On Diophantine triples of Pell numbers
Volume 156 / 2019
Colloquium Mathematicum 156 (2019), 273-285
MSC: 11D09, 11D45, 11B37, 11J86.
DOI: 10.4064/cm7387-7-2018
Published online: 1 February 2019
Abstract
Let $P_m$ be the $m$th Pell number. We prove that if $2P_{2n}P_k+1$ and $2P_{2n+2}P_k+1$ are both perfect squares, then $k=2n$ or $k=2n+2$ for $n\geq 1$.
