Florian Luca, Pantelimon Stanica: Equations with arithmetic functions of Pell numbers, p.409-413

Abstract:

Here, we prove some diophantine results about the Euler function of Pell numbers and their Pell-Lucas companion sequence. For example, if the Euler function of the $n$th Pell number $P_n$ or Pell-Lucas companion number $Q_n$ is a power of $2$, then $n\le 8$.

Key Words: Euler function, Pell numbers.

2000 Mathematics Subject Classification: Primary: 11B39;
Secondary: 11A25.

Download the paper in pdf format here.