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Edit: The $F$'s are Fibonacci numbers.

I need an idea on how to show the following:

If $m$ and $n$ are positive integers, then $(F_m,F_n)=F_{(m,n)}$.

I believe that using the fact that $F_{m+n}=F_mF_{n+1}+F_nF_{m-1}$ could come in handy. Moreover, Euclid's algorithm may as well be needed. But I am not certain, as there may be better methods to achieve this.

Thanks in advance.

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    I understand now. :) Thanks, guys!2012-04-25

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As noted in the comments by sdcvvc, this answer to an earlier question completely answers this question as well.