# Fibonacci

Algebra Level 5

Let $$F_n = F_{n-1}+ F_{n-2}$$ be the $$n$$th Fibonacci number ($$n>0)$$, where $$F_1=1$$ and $$F_2=1$$. Find the smallest $$F_n$$ such that $$1 000 \mid F_n$$. Give $$n$$ as the answer.

Bonus: How many digits this $$F_n$$ has?

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