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} }
2 Citations
Base phi representations and golden mean beta-expansions
- Mathematics
- 2019
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
- MathematicsJ. 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.
References
SHOWING 1-6 OF 6 REFERENCES
On Real Quadratic Number Fields and Simultaneous Diophantine Approximation
- Mathematics
- 1999
Abstract. Here we provide a necessary and sufficient condition on the partial quotients of two real quadratic irrational numbers to insure that they are elements of the same quadratic number field…
COMBINATORIAL PROOFS OF ZECKENDORF FAMILY IDENTITIES
- Mathematics
- 2009
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…
Exploring the Number Jungle: A Journey into Diophantine Analysis
- Mathematics
- 2000
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
- Mathematics
- 1957
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…