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arXiv · 2509.16150

New properties of the $\varphi$-representation of integers

Jeffrey Shallit·Ingrid Vukusic
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Abstract

We prove a few new properties of the $\varphi$-representation of integers, where $\varphi = (1+\sqrt{5})/2$. In particular, we prove a 2012 conjecture of Kimberling. As software assistants, we used the Walnut theorem-prover, and in one proof, ChatGPT 5.

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Jeffrey Shallit, Ingrid Vukusic. 2025-09-19. New properties of the $\varphi$-representation of integers. https://arxiv.org/abs/2509.16150

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