Canonical Diophantine representations of natural numbers with respect to quadratic “bases”☆

@article{Burger2013CanonicalDR,
  title={Canonical Diophantine representations of natural numbers with respect to quadratic “bases”☆},
  author={Edward B. Burger and David C. Clyde and Cory H. Colbert and Gea Hyun Shin and Zhaoning Wang},
  journal={Journal of Number Theory},
  year={2013},
  volume={133},
  pages={1372-1388}
}

Base phi representations and golden mean beta-expansions

In the base phi representation any natural number is written uniquely as a sum powers of the golden mean with digits 0 and 1, where one requires that the product of two consecutive digits is always

The Fibonacci Sequence and Schreier-Zeckendorf Sets

  • H. Chu
  • Mathematics
    J. Integer Seq.
  • 2019
The Fibonacci sequence is discovered by counting the number of subsets of $\{1,2,\ldots, n\}$ such that two consecutive elements in increasing order always differ by an odd number.

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A general combinatorial approach is presented for proving identities of the form mfn = P i2Im fn+i, where m is a nonnegative integer constant, n ‚ jmin(Im)j is an integer, Im is a set of

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Opening thoughts: Welcome to the jungle A bit of foreshadowing and some rational rationale Building the rationals via Farey sequences Discoveries of Dirichlet and Hurwitz The theory of continued

A Number System with an Irrational Base

Editors' Note: This article was written by the author when he was a 12-year old student at Junior High School 246 in Brooklyn, New York. Here he explores using the golden mean, which he calls τ, more