 Cassini's identity

For the Fibonacci numbers $F_0=0$, $F_1=1$, the identity $F_{n+1}{F}_{n-1}-F_n^2=(-1{)}^n$ holds for $n\ge 1$. It follows by induction: replacing each term using the Fibonacci recurrence negates the left-hand side when $n$ increases by one, and the value at $n=1$ is $-1$.