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
2026-04-04 02:35:10.1775270110
Greatest Common Divisor with Fibonacci Numbers
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The Euclidean algorithm, $\gcd(a,b)=\gcd(a-b,b)$ works well with the Fibonacci recurrence.