Theorem T12 Let FnF_nFn be the Fibonacci numbers. Then Fn+m=FmFn+1+Fm−1Fn ,m≥1,n≥0.F_{n+m} = F_m F_{n+1} + F_{m-1} F_n \;, \quad m \geq 1, n \geq 0. Fn+m=FmFn+1+Fm−1Fn,m≥1,n≥0.