Difference between revisions of "Catalan's identity"

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The following formula holds:
 
The following formula holds:
 
$$F_n^2 - F_{n+r} F_{n-r} = (-1)^{n-r}F_r^2,$$
 
$$F_n^2 - F_{n+r} F_{n-r} = (-1)^{n-r}F_r^2,$$
where $F_n$ denotes a [[Fibonacci sequence|Fibonacci number]].  
+
where $F_n$ denotes a [[Fibonacci numbers|Fibonacci number]].  
  
 
==Proof==
 
==Proof==

Revision as of 00:30, 24 May 2017

Theorem

The following formula holds: $$F_n^2 - F_{n+r} F_{n-r} = (-1)^{n-r}F_r^2,$$ where $F_n$ denotes a Fibonacci number.

Proof

See also

Cassini's identity

References