The Chung-Graham Expansion
Number Theory
2025-04-02 v1
Abstract
Chung and Graham introduced a method to uniquely represent each positive integer using even-indexed Fibonacci terms. We generalize this result to represent each positive integer using other Fibonacci terms with equally-spaced indices.
Cite
@article{arxiv.2504.00314,
title = {The Chung-Graham Expansion},
author = {Sungkon Chang},
journal= {arXiv preprint arXiv:2504.00314},
year = {2025}
}
Comments
A shorter version is accepted by Elemente der Mathematik, under the title "Expansions of positive integers in terms of Fibonacci terms with equally-spaced indices."