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Proposition 14. The Fibonacci numbers are defined to be F1 = F2 = 1 and F, = Fn-1+ Fn-2 for n > 3. The nth Fibonacci number Fn is even if and only if 3|n. Hint: Try induction. You could induct on n or in the case where 3|n you could induce on k where n = 3k. Proof.

Proposition 14. The Fibonacci numbers are defined to be F1 = F2 = 1 and F, = Fn-1+ Fn-2 for n > 3. The nth Fibonacci number Fn is even if and only if 3|n. Hint: Try induction. You could induct on n or in the case where 3|n you could induce on k where n = 3k. Proof.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Proposition 14. The Fibonacci numbers are defined to be F1 = F2 = 1 and Fn n 2 3. The nth Fibonacci number Fn is even if and only if 3|n. Fn-1 + Fn-2 for Hint: Try induction. You could induct on n or in the case where 3| you could induce on k where n = 3k. Proof.
Transcribed Image Text:Proposition 14. The Fibonacci numbers are defined to be F1 = F2 = 1 and Fn n 2 3. The nth Fibonacci number Fn is even if and only if 3|n. Fn-1 + Fn-2 for Hint: Try induction. You could induct on n or in the case where 3| you could induce on k where n = 3k. Proof.
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