Question: Recall that the Fibonacci sequence is defined by starting with F = 1, F = 1, and then via the recurrence relation Fn =

Recall that the Fibonacci sequence is defined by starting with F =

Recall that the Fibonacci sequence is defined by starting with F = 1, F = 1, and then via the recurrence relation Fn = Fn-1 + Fn-2 for all n 2. Prove by induction that the nth Fibonacci number Fn is even if and only if n = 0 (mod 3).

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We will prove this statement by induction on n Base case n 0 Here F 0 1 is odd and 0 is congruent to ... View full answer

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