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Claim: $L_n=F_{n-1}+F_{n+1}$ for all $n >0$

Could someone please help me prove this? My professor mentioned it in class, but didn't show us how to prove it. I am just curious. The $L$ stands for the Lucas numbers and the $F$ stands for the Fibonacci numbers.

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Have you tried anything? – Ahaan S. Rungta Nov 23 '13 at 3:14
I don't even know where to start. – A Glenn Nov 23 '13 at 3:17

The exact statement should be:


Prove it by Induction.

$P(1)$ and $P(2)$ are easy to check.

Then $P(n-1), P(n) \Rightarrow P(n+1)$ is easy:


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