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This is always possible, because 1 is a Fibonacci number.
by eapriv 2y ago
This is always possible, because 1 is a Fibonacci number.
- sorokod 2y agoThat is true, the article skips the fact that the approximation using the initial fib numbers is not useful.
- gilleain 2y agofrom the wiki page: "Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers." so, distinct and non-consecutive
- eapriv 2y agoSure, but the conversion method does not require the numbers to be distinct or non-consecutive.
- muti 2y agoNon consecutive isn't surprising, any consecutive Fibonacci numbers in the sum can be replaced with their sum, which is itself a Fibonacci number by definition
- lupire 2y agoThat's not sufficient to be unsurprising. What if a sum has more than 2 consecutive Fibonacci numbers? That doesn't cause a problem, but it takes a little more work to sort it out.
- muti 2y agoI find the distinct property much more interesting and non obvious. It looks like non consecutivity is only there to force unique solutions hence called zeckendorf representations