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The Fibonacci numbers are defined recursively as follows: f0 = 0, f1 = 1 and fn...

The Fibonacci numbers are defined recursively as follows: f0 = 0, f1 = 1 and fn = fn−1 + fn−2 for all n ≥ 2.

Prove that for all non-negative integers n: fn*fn+2 = ((fn+1))^ 2 − (−1)^n

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