# Golden Fibonacci

Number Theory Level 5

$\lim _{ n\rightarrow \infty }{ \frac { 2{ F }_{ n+8 } }{ { F }_{ n } } } ={ F }_{ \alpha }\sqrt { { F }_{ \beta } } +{ F }_{ \gamma }-F_{ \delta }$ Let $$F_n$$ denote the $$n^\text{th}$$ Fibonacci number. Find $$\alpha +\beta +\gamma +\delta$$.

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