Find The 46th Fibonacci Number

Consider the Fibonacci sequence, defined as follows:

Fibonacci(1) = 1
Fibonacci(2) = 1
Fibonacci(n) = Fibonacci(n - 2) + Fibonacci(n - 1)

The first two Fibonacci numbers are 1, 1. The following elements are computed by adding the prior two.

The first 6 Fibonacci numbers are: 1, 1, 2, 3, 5, 8.

Let F be the \(46^\text{th}\) Fibonacci number. What are the last 3 digits of F?

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