  Let $ \{F_n\}_{n\ge 0} $ be the sequence of Fibonacci numbers and let $p$ be
a prime. For an integer $c$ we write $m_{F,p}(c)$ for the number of distinct
representations of $c$ as $F_k-p^\ell$ with $k\ge 2$ and $\ell\ge 0$. We prove
that $m_{F,p}(c)\le 4$.
