Catalan’s identity

Let $f_n$ be the nth Fibonacci number $n>1$, then the following identity is called Catalan’s identity.

$$f_n^2-f_{n+r}{f}_{n-r}={(-1)}^{n-r}{f}_r^2.$$

For $r=1$ we have Cassini’s identity.

Title	Catalan’s identity
Canonical name	CatalansIdentity
Date of creation	2013-03-22 14:42:56
Last modified on	2013-03-22 14:42:56
Owner	vmoraru (1243)
Last modified by	vmoraru (1243)
Numerical id	7
Author	vmoraru (1243)
Entry type	Theorem
Classification	msc 11B39
Related topic	ProofofCassinisIdentity