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- Zeckendorf's_theorem abstract "Zeckendorf's theorem, named after Belgian mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers.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. More precisely, if N is any positive integer, there exist positive integers ci ≥ 2, with ci + 1 > ci + 1, such that where Fn is the nth Fibonacci number. Such a sum is called the Zeckendorf representation of N. The Fibonacci coding of N can be derived from its Zeckendorf representation.For example, the Zeckendorf representation of 100 is 100 = 89 + 8 + 3.There are other ways of representing 100 as the sum of Fibonacci numbers – for example100 = 89 + 8 + 2 + 1100 = 55 + 34 + 8 + 3but these are not Zeckendorf representations because 1 and 2 are consecutive Fibonacci numbers, as are 34 and 55.For any given positive integer, a representation that satisfies the conditions of Zeckendorf's theorem can be found by using a greedy algorithm, choosing the largest possible Fibonacci number at each stage.".
- Zeckendorf's_theorem thumbnail Zeckendorf_representations.png?width=300.
- Zeckendorf's_theorem wikiPageExternalLink fibnim.
- Zeckendorf's_theorem wikiPageID "1377405".
- Zeckendorf's_theorem wikiPageRevisionID "592147042".
- Zeckendorf's_theorem author "G.M. Phillips".
- Zeckendorf's_theorem hasPhotoCollection Zeckendorf's_theorem.
- Zeckendorf's_theorem id "8810".
- Zeckendorf's_theorem name "Knuth's Fibonacci product".
- Zeckendorf's_theorem sequencenumber "A101330".
- Zeckendorf's_theorem title "Zeckendorf Representation".
- Zeckendorf's_theorem title "Zeckendorf representation".
- Zeckendorf's_theorem title "Zeckendorf's Theorem".
- Zeckendorf's_theorem title "proof that the Zeckendorf representation of a positive integer is unique".
- Zeckendorf's_theorem urlname "Z/z120020".
- Zeckendorf's_theorem urlname "ZeckendorfRepresentation".
- Zeckendorf's_theorem urlname "ZeckendorfsTheorem".
- Zeckendorf's_theorem subject Category:Articles_containing_proofs.
- Zeckendorf's_theorem subject Category:Fibonacci_numbers.
- Zeckendorf's_theorem subject Category:Theorems_in_number_theory.
- Zeckendorf's_theorem type Abstraction100002137.
- Zeckendorf's_theorem type Amount105107765.
- Zeckendorf's_theorem type Attribute100024264.
- Zeckendorf's_theorem type Communication100033020.
- Zeckendorf's_theorem type FibonacciNumbers.
- Zeckendorf's_theorem type Magnitude105090441.
- Zeckendorf's_theorem type Message106598915.
- Zeckendorf's_theorem type Number105121418.
- Zeckendorf's_theorem type Property104916342.
- Zeckendorf's_theorem type Proposition106750804.
- Zeckendorf's_theorem type Statement106722453.
- Zeckendorf's_theorem type Theorem106752293.
- Zeckendorf's_theorem type TheoremsInNumberTheory.
- Zeckendorf's_theorem comment "Zeckendorf's theorem, named after Belgian mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers.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.".
- Zeckendorf's_theorem label "Stelling van Zeckendorf".
- Zeckendorf's_theorem label "Teorema di Zeckendorf".
- Zeckendorf's_theorem label "Théorème de Zeckendorf".
- Zeckendorf's_theorem label "Twierdzenie Zeckendorfa".
- Zeckendorf's_theorem label "Zeckendorf's theorem".
- Zeckendorf's_theorem label "ゼッケンドルフの定理".
- Zeckendorf's_theorem label "齊肯多夫定理".
- Zeckendorf's_theorem sameAs Théorème_de_Zeckendorf.
- Zeckendorf's_theorem sameAs Teorema_di_Zeckendorf.
- Zeckendorf's_theorem sameAs ゼッケンドルフの定理.
- Zeckendorf's_theorem sameAs Stelling_van_Zeckendorf.
- Zeckendorf's_theorem sameAs Twierdzenie_Zeckendorfa.
- Zeckendorf's_theorem sameAs m.04xx7j.
- Zeckendorf's_theorem sameAs Q1188392.
- Zeckendorf's_theorem sameAs Q1188392.
- Zeckendorf's_theorem sameAs Zeckendorf's_theorem.
- Zeckendorf's_theorem wasDerivedFrom Zeckendorf's_theorem?oldid=592147042.
- Zeckendorf's_theorem depiction Zeckendorf_representations.png.
- Zeckendorf's_theorem isPrimaryTopicOf Zeckendorf's_theorem.
