https://github.com/chrisdalvit/zeckendorf-theorem
A formal proof of the Zeckendorf theorem in Isabelle/HOL
https://github.com/chrisdalvit/zeckendorf-theorem
fibonacci-numbers fibonacci-sequence formal-verification isabelle isabelle-hol number-theory theorem-proving theoretical-computer-science
Last synced: 5 months ago
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A formal proof of the Zeckendorf theorem in Isabelle/HOL
- Host: GitHub
- URL: https://github.com/chrisdalvit/zeckendorf-theorem
- Owner: chrisdalvit
- Created: 2023-05-02T15:31:40.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2023-06-15T16:03:34.000Z (about 3 years ago)
- Last Synced: 2025-12-07T13:19:24.276Z (7 months ago)
- Topics: fibonacci-numbers, fibonacci-sequence, formal-verification, isabelle, isabelle-hol, number-theory, theorem-proving, theoretical-computer-science
- Language: TeX
- Homepage: https://www.isa-afp.org/entries/Zeckendorf.html
- Size: 27.4 MB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# Zeckendorf's Theorem
This work formalizes Zeckendorf's theorem in Isabelle/HOL. The theorem states that every positive integer can be uniquely represented as a sum of one or more non-consecutive Fibonacci numbers. More precisely, if
$N$ is a positive integer, there exist unique positive integers $c_i \ge 2$ with $c_i + 1 < c_{i+1}$, such that
$$N = \sum_{i=0}^{k} F_{c_i}$$
where $F_n$ is the $n$-th Fibonacci number.