How to show that the Fibonacci sequence is a divisibility sequence?

[FallArk]

I wanted to prove that the Fibonacci sequence is a divisibility sequence, but I don't even know how to prove it.
all I know is that $$gcd\left({F}_{m},{F}_{n}\right)={F}_{gcd\left(m,n\right)}$$ and I should somehow use the Euclidean algorithm?

 

[FallArk]

I found this on stack exchange
https://math.stackexchange.com/questions/60340/fibonacci-modular-results