Fibonacci 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

The 7th rightmost digit in 32 consecutive Fibonacci numbers are all 0's.

Let \(F_n\) be the smallest Fibonacci number that can be the first of such a sequence of 32 Fibonacci numbers. Find \(n\).

Note: \(F_0 = 0, F_1 = F_2 = 1 \).

Inspiration.

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