New properties of the $\varphi$-representation of integers
Number Theory
2026-03-12 v2 Formal Languages and Automata Theory
Abstract
We prove a few new properties of the -representation of integers, where . In particular, we prove a 2012 conjecture of Kimberling. As software assistants, we used the Walnut theorem-prover, and in one proof, ChatGPT 5.
Cite
@article{arxiv.2509.16150,
title = {New properties of the $\varphi$-representation of integers},
author = {Jeffrey Shallit and Ingrid Vukusic},
journal= {arXiv preprint arXiv:2509.16150},
year = {2026}
}