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  3. 1 let fnngt1 denote the fibonacci sequence ie f1f21 and...

Question: 1 let fnngt1 denote the fibonacci sequence ie f1f21 and...

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1. Let {Fn}n>1 denote the Fibonacci sequence, i.e., F1-F2-1 and Fn+2 = Fn+1 + F, for n 2 1. (a) [3 points] Show that gcd(Fn+1,%) gcd(F,, Fn-1) for every n > 2. Using this relation, prove that gcd(F+1, F) 1 for every n2 1 (b) [2 points] Using induction, prove that Fan is an even integer for every n21.

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