For let be the Fibonacci number :

Prove that :

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- Feb 27th 2010, 10:46 PMflower3Fibonacci number
For let be the Fibonacci number :

Prove that :

- Feb 27th 2010, 11:53 PMchisigma
According to...

Fibonacci number - Wikipedia, the free encyclopedia

... a basic property of the fibonacci's numbers is that 'every 3rd number of the sequence is even and more generally, every k-th number of the sequence is a multiple of '. In case of is ...

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- Feb 28th 2010, 12:05 AMalexmahone
**Proof by induction:**

Let the statement be P(n).

Thus P(3) is true.

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Let P(m) be true.

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Consider P(m+3).

Thus 3 divides m+3.

Thus is even.

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Hence, by the principle of induction, the statement is true.