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.
