Cassini's Identity

For $F_n$ the $n$th Fibonacci Number,

$$F_{n-1}F_{n+1}-{F_n}^2=(-1)^n.$$

See also Fibonacci Number

References

Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, p. 12, 1996.