MMN-2131
Balancing with powers of the Lucas sequence of recurrence $u_{n}=Au_{n-1}-u_{n-2}$
Nurettin Irmak; Murat Alp;Abstract
In this paper, we show that there is no solution of the diophantine equation
u_{1}^{k}+u_{2}^{k}+\cdots u_{n-1}^{k}=u_{n+1}^{l}+u_{n+2}^{l}+\cdots
u_{n+r}^{l}
for special cases of $k$ and $l$ where the elements of sequence $\left\{ u_{n}\right\} $ satisfy the relation $u_{n}=Au_{n-1}-u_{n-2} $ with $u_{0}=0$ and $u_{1}=1$.
Vol. 18 (2017), No. 2, pp. 851-858