Recall that the Fibonacci sequence is defined by starting with F = 1, F = 1,...

Transcribed Image Text:

Recall that the Fibonacci sequence is defined by starting with F₁ = 1, F₂ = 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). Recall that the Fibonacci sequence is defined by starting with F₁ = 1, F₂ = 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).

Answer rating: 100% (QA)

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 the full answer