KöMaL 2011 B4394

Consider the Fibonacci sequence defined by the recursive formula $F_1$=$F_2$=1, $F_n$=$F_{n-1}$+$F_{n-2}$. Prove that if $k$<$m$, then $\sum_{i=k}^{m} F_i F_{i+3}$ is a composite number.