Theorem T10 Let FnF_nFn be the Fibonacci numbers. Then Fn+1Fn−1−Fn2=(−1)n ,n≥1.F_{n+1} F_{n-1} - F_n^2 = (-1)^n \;, \quad n \geq 1. Fn+1Fn−1−Fn2=(−1)n,n≥1.