Cassini's Identity

Theorem
Let $F_k$ be the $k$th Fibonacci number.

Then:
 * $F_{n + 1} F_{n - 1} - F_n^2 = \paren {-1}^n$

Also reported as
This is also sometimes reported (slightly less elegantly) as:
 * $F_{n + 1}^2 - F_n F_{n + 2} = \paren {-1}^n$