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

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FallArk
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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?
 

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