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

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

This appears to be very similar to, if not the same as Vajda's identity,

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

Reference: Cassini and Catalan identities.


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