Catalan's identity
From specialfunctionswiki
Theorem
The following formula holds: $$F(n)^2 - F(n+r) F(n-r) = (-1)^{n-r}F(r)^2,$$ where $F(n)$ denotes the $n$th Fibonacci number.
The following formula holds: $$F(n)^2 - F(n+r) F(n-r) = (-1)^{n-r}F(r)^2,$$ where $F(n)$ denotes the $n$th Fibonacci number.
