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  3. 1 let fn21 denote the fibonacci sequence ie fi f21...

Question: 1 let fn21 denote the fibonacci sequence ie fi f21...

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1. Let {F,.)n21 denote the Fibonacci sequence, i.e., Fi F2-1 and Fm2 i + F, for n 21. (a) [3 points] Show that ged(Futl, F)-ged(F F-1) for every n 22. Using this relation, prove that ged(Fn+1, Fn) 1 for every n 2 1. (b) [2 points] Using induction, prove that Fan is an even integer for every n 2 1.

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