Consider the sequence F₁, F2, F3, . . ., where F₁ = 1, F₂ = 1, F3 = 2, F4 = 3, F5 = 5 and F6 = 8. The terms of this sequence are called Fibonacci numbers. Prove that 2 | F if and only if 3 | n.

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Consider the sequence F1, F2, F3, . . ., where
F₁ = 1, F₂ = 1, F3 = 2, F4 = 3, F5 = 5 and F6 = 8.
The terms of this sequence are called Fibonacci numbers.
Prove that 2 | F if and only if 3 | n.
Transcribed Image Text:Consider the sequence F1, F2, F3, . . ., where F₁ = 1, F₂ = 1, F3 = 2, F4 = 3, F5 = 5 and F6 = 8. The terms of this sequence are called Fibonacci numbers. Prove that 2 | F if and only if 3 | n.
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