Prove F_2n = FnLn, where Fn are fibonacci numbers and Ln are Lucas numbers.

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- Feb 4th 2007, 03:26 PMyc6489Prove F_2n = FnLn
Prove F_2n = FnLn, where Fn are fibonacci numbers and Ln are Lucas numbers.

- Feb 4th 2007, 05:01 PMThePerfectHacker
- Feb 4th 2007, 09:20 PMSoroban
Hello, yc6489!

Quote:

Prove: . ,

where are Fibonacci numbers and are Lucas numbers.

Are we allowed to use the*closed forms*for and ?

. .

Then: .

. .

- Feb 5th 2007, 12:25 PMyc6489
Thanks Soroban for your reply. I think the intention of the exercise is to prove the statement from the definition of Ln = F_n-1 + F_n+1 for n>=2. (The text does not mention your particular definitions of Fn and Ln.)

- Feb 5th 2007, 01:08 PMThePerfectHacker