Six equations in search of a finite-fold-ness proof
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917790050418688 |
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| author | Cantone, Domenico Cuzziol, Luca Omodeo, Eugenio G. |
| author_facet | Cantone, Domenico Cuzziol, Luca Omodeo, Eugenio G. |
| contents | By following the same construction pattern which Martin Davis proposed in a 1968 paper of his, we have obtained six quaternary quartic Diophantine equations that candidate as `rule-them-all' equations: proving that one of them has only a finite number of integer solutions would suffice to ensure that each recursively enumerable set admits a finite-fold polynomial Diophantine representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02208 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Six equations in search of a finite-fold-ness proof Cantone, Domenico Cuzziol, Luca Omodeo, Eugenio G. Number Theory Logic 03D25, 11D25 By following the same construction pattern which Martin Davis proposed in a 1968 paper of his, we have obtained six quaternary quartic Diophantine equations that candidate as `rule-them-all' equations: proving that one of them has only a finite number of integer solutions would suffice to ensure that each recursively enumerable set admits a finite-fold polynomial Diophantine representation. |
| title | Six equations in search of a finite-fold-ness proof |
| topic | Number Theory Logic 03D25, 11D25 |
| url | https://arxiv.org/abs/2303.02208 |