# Identity relating Fibonacci sequence

Is this identity known. If $F_n$ is the $n$-th Fibonacci number then $$F_{n+ m+r}F_n - F_{n+m}F_{n+r}=(-1)^{n-1}F_mF_r$$.

• Is that $\forall m,r \in\mathbb{N}$? Or are there more restrictions? – mrnovice Apr 23 '17 at 21:04

$$F_{n+i}F_{n+j} - F_{n}F_{n+i+j} = (-1)^nF_{i}F_{j}$$