Let $(F_n )_{n\ge o}$ be the sequence of Fibonacci numbers: $F_0 = 0$, $F_1 = 1$ and $F_{n+2} = F_{n+1}+F_n$ , for every $n \ge 0$. Prove that for any prime $p \ge 3$, $p$ divides $F_{2p} - F_p$ .