Define a function f by f (1) = 1, f (2) = 1, and f (n) = f (n − 1) + f (n − 2) for all positive integers n ≥ 2. The function f generates the Fibonacci sequence of numbers.
a. Find the first 10 Fibonacci numbers.
b. Show that for any positive integer n, the only positive integer d that divides both Fn and Fn+1 is d = 1.
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