On the Diophantine equation $F_n=F_l^k(F_l^m-1)$

The sequence $\{F_t\}_{t=0}^{\infty}$ refers to the Fibonacci sequence, defined by the recurrence formula $F_t=F_{t-1}+F_{t-2}$, for $t\geq 2$, with the initial conditions $F_0=0$ and $F_1=1$. In this paper, we establish that the only solution to the Diophantine equation $$F_n=F_l^k (F_l^m - 1)$$ is $(n,l,k,m)=(6,3,3,1)$, where $n,m\geq 1$, $k\geq 2$, and $l\geq 3$.