  Let us denote by $F_n$ the $n$-th Fibonacci number. In this paper we show
that for a fixed integer $y$ there exists at most one integer exponent $a>0$
such that the Diophantine equation $F_n+F_m=y^a$ has a solution $(n,m,a)$ in
positive integers satisfying $n>m>0$, unless $y=2,3,4,6$ or $10$.
