Power of Two as sums of Three Pell Numbers

Abstract

In this paper, we find all the solutions of the Diophantine equation $P_{\ell }+P_m+P_n=2^a$, in nonnegative integer variables $(n,m,\ell ,a)$ where $P_k$ is the $k$-th term of the Pell sequence $\{P_n{\}}_{n\ge 0}$ given by $P_0=0$, $P_1=1$ and $P_{n+1}=2P_n+P_{n-1}$ for all $n\ge 1$.

10 pages