Zhi-Wei Sun's 1-3-5 Conjecture and Variations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Acceso en línea: | |
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| _version_ | 1866912522249961472 |
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| author | Machiavelo, António Tsopanidis, Nikolaos |
| author_facet | Machiavelo, António Tsopanidis, Nikolaos |
| contents | In this paper, using quaternion arithmetic in the ring of Lipschitz integers, we present a proof of Zhì-Wěi Sūn's "1-3-5 conjecture" for integral solutions, and for all natural numbers greater than a specific constant. This, together with computations done by the authors and a colleague, which checked the validity of the conjecture up to that constant, completely proves the 1-3-5 conjecture. We also establish some variations of this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_02592 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Zhi-Wei Sun's 1-3-5 Conjecture and Variations Machiavelo, António Tsopanidis, Nikolaos Number Theory In this paper, using quaternion arithmetic in the ring of Lipschitz integers, we present a proof of Zhì-Wěi Sūn's "1-3-5 conjecture" for integral solutions, and for all natural numbers greater than a specific constant. This, together with computations done by the authors and a colleague, which checked the validity of the conjecture up to that constant, completely proves the 1-3-5 conjecture. We also establish some variations of this conjecture. |
| title | Zhi-Wei Sun's 1-3-5 Conjecture and Variations |
| topic | Number Theory |
| url | https://arxiv.org/abs/2003.02592 |