### Abstract

This work formalizes Zeckendorf's theorem. 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.

### License

BSD License

### Topics

- Mathematics/Number theory

### Session Zeckendorf

- Zeckendorf

## Cite

×

Zeckendorf-AFP

    @article{Zeckendorf-AFP,
      author  = {Christian Dalvit},
      title   = {Zeckendorf’s Theorem},
      journal = {Archive of Formal Proofs},
      month   = {June},
      year    = {2023},
      note    = {\url{https://isa-afp.org/entries/Zeckendorf.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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