  In this paper, we study the solutions of the equation $F_n-F_m=p^a$ where $p$
is either $7$ or $13$ and $n>m\geqslant 0$, $a\geqslant 2$. We confirm the
conjecture of Erduvan and Keskin by proving that there is no solutions for this
Diophantine equation. We will use the lower bounds for linear forms in
logarithms (Baker's theory) and a version of the Baker-Davenport reduction
method in Diophantine approximation.
