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Empty
 one year ago
Prove that any number \(x \in \mathbb{N} \) can be represented uniquely by the sum of unique Fibonacci numbers that are NOT consecutive.
Empty
 one year ago
Prove that any number \(x \in \mathbb{N} \) can be represented uniquely by the sum of unique Fibonacci numbers that are NOT consecutive.

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Empty
 one year ago
Best ResponseYou've already chosen the best response.1I guess it gives it away to say this is called Zeckendorf's theorem. Rofl I just discovered this and thought it sounded cool.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1Things that are on my mind right now:  Induction  Creating various independent sequences of numbers that have no term in common and also that their union is \(\mathbb N\)

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Let's just try to figure out this proof together here: https://en.wikipedia.org/wiki/Zeckendorf's_theorem#Proof

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1Oh, great. I got the induction thing right.

Empty
 one year ago
Best ResponseYou've already chosen the best response.1I feel like understanding how someone could prove such a crazy statement as this would lead us to understanding some pretty interesting stuff haha.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1Stronginduction is really mindboggling. It's amazing how well it works if you don't know how to prove things.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1How did they even come up with that proof? The uniqueness one is even worse.

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Yeah this is pretty much too crazy for me, I wonder if numberphile did a video on this or if there's a youtube video of someone explaining it to me
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