$F_1=F_2=1; F_{n+2}=F_{n+1}+F_n,\,n\ge1$

Find the smallest integer $k$ such that the 4 last digits of $F_k$ is 2016.

The answer is 1068.

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Using Excel, computed $G_n = (G_{n-1}+G_{n-2})\text{ mod }10000$ for first 2000 n, find out that $G_n = 2016 \text{ where }n = \boxed{1068}$ .