In: Advanced Math
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?