MathNumber theory

Euclid's algorithm

Theory

Fibonacci numbers

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The Fibonacci numbers F0,F1,…F_{0}, F_{1}, \ldots are given by the recurrenceFn+1=Fn+Fn−1,F0=0,F1=1F_{n+1} = F_{n} + F_{n−1}, \quad F_{0} = 0, F_{1} =1 How many recursive calls will Euclid's algorithm make to find gcd⁡(F999,F998)\gcd(F_{999}, F_{998})?

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