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Prove that for all integers $n\geq 0$:

$$\gcd(F_{n+1},F_n)=1$$

I am extremely lost. Please can some provide some hint or direction? Thank you so very much

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The Euclidean algorithm, $\gcd(a,b)=\gcd(a-b,b)$ works well with the Fibonacci recurrence.

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  • $\begingroup$ Thank you so much!!!!!!!!!!!! $\endgroup$
    – gordon sung
    Feb 24, 2016 at 6:26

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