Homework Help: Fibonacci sequence, division

1. Nov 12, 2006

mattmns

Here is the question:
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Prove that $f_{n}$ is even if and only if n is divisible by 3. ($f_{n}$ is of course the nth Fibonacci number)
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Proving that n is divisible by 3 => $f_{n}$ is even is easily done by induction, but the other implication is eluding me. It is easy to show that $f_{n}$ is even iff $f_{n-3}$ is even, but I can't see if this helps. Any ideas about how to prove this implication? Thanks.

2. Nov 12, 2006

slearch

If this is easy to show, then it would be enough to look at the evenness of $$f_0, f_1$$, and $$f_2$$.

3. Nov 12, 2006

mattmns

I was thinking about that, and I think you are absolutely right. Thanks.