Divisibility of Fibonacci Number/Corollary

Corollary to Divisibility of Fibonacci Number
Let $F_k$ denote the $k$th Fibonacci number.

Then:
 * $\forall m, n \in \Z_{> 0}: F_m \mathrel \backslash F_{m n}$

where $\mathrel \backslash$ denotes divisibility.

Proof
When $m = 1$ or $n = 1$ the result is trivially true.

Otherwise, by definition of divisibility:
 * $m \mathrel \backslash m n$

and the result follows from Divisibility of Fibonacci Number.