Fibonacci numbers are defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 +...

Fibonacci numbers are defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 + Fn for all n ∈ N ∪ {0}.

(1) Make and prove an (if and only if) conjecture about which Fibonacci numbers are multiples of 3.
(2) Make a conjecture about which Fibonacci numbers are multiples of 2020. (You do not need to prove your

conjecture.) How many base cases would a proof by induction of your conjecture require?

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Colby Messinger answered 1 year ago

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