Fibonacci numbers. how to prove? [duplicate]

We are give Fibonacci numbers.{fi | i ∈ N}, where f0 = 0, f1 = 1, fn+2 = fn +fn+1, n∈ N. How to proof with mathematical induction that if n divides by m, then fn divides by fm? I am having trouble with thinking, what should be the transition.

• Hi & welcome to MSE. Please show us what you've tried so far & are having difficulty with. Thanks. – John Omielan Dec 27 '18 at 23:29

First prove by induction on $$m$$ that
$$F_{m+n}=F_{m+1}F_n+F_mF_{n+1}-F_m F_n$$
Then put $$m=kn$$ and find that if $$F_n|F_{kn}$$ then $$F_n|F_{(k+1)n}$$.