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We define the Fibonacci numbers as follows: F1 = F2 = 1 and F(n 2) = F(n 1) F(n) for all n > 1. Prove the following statements by induction: F(2n) F(2n 1) = F(n 1)^2 and F(2n)F(2n 1) F(2n 1)^2 = F(2n 2).
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