# 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.

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