1
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Is that $\forall m,r \in\mathbb{N}$? Or are there more restrictions? $\endgroup$ – mrnovice Apr 23 '17 at 21:04
2
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.