New properties of the $φ$-representation of integers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908878751399936 |
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| author | Shallit, Jeffrey Vukusic, Ingrid |
| author_facet | Shallit, Jeffrey Vukusic, Ingrid |
| contents | We prove a few new properties of the $φ$-representation of integers, where $φ= (1+\sqrt{5})/2$. In particular, we prove a 2012 conjecture of Kimberling. As software assistants, we used the Walnut theorem-prover, and in one proof, ChatGPT 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New properties of the $φ$-representation of integers Shallit, Jeffrey Vukusic, Ingrid Number Theory Formal Languages and Automata Theory We prove a few new properties of the $φ$-representation of integers, where $φ= (1+\sqrt{5})/2$. In particular, we prove a 2012 conjecture of Kimberling. As software assistants, we used the Walnut theorem-prover, and in one proof, ChatGPT 5. |
| title | New properties of the $φ$-representation of integers |
| topic | Number Theory Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2509.16150 |