- #1

rumborak

- 706

- 154

Can any natural number be construed by a sum of unique Fibonacci numbers?

My guess was yes, and a C program I wrote confirms that to be up to about 2,000, but that's of course is no proof. The best semi-proof I could come up with is that the Fibonacci sequence is more closely than the power-of-two sequence, which we know is enough to construct all numbers. Better explanation, but still a bit hand-wavy.