Problem #WSP-000115

Problem

Prove for any integers $m, n \geq 0$ that $F_{m + n} = F_{m - 1} F_{n} + F_{m} F_{n + 1}$ .
Corollary: if $k ∣ n$ , then $F_{k} ∣ F_{n}$ . This can be proven by induction if we write $n = s k$ for a natural $s$ , then $F_{k + (s - 1) k} = F_{k - 1} F_{(s - 1) k} + F_{k} F_{(s - 1) k + 1} .$

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