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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2402.06567 |
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| _version_ | 1866908499527598080 |
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| author | Ulas, Maciej |
| author_facet | Ulas, Maciej |
| contents | In this note we consider the title Diophantine equation from both theoretical as well as experimental point of view. In particular, we prove that for $k=4, 6$ and each choice of the signs our equation has infinitely many co-prime positive integer solutions. For $k=5, 7$ and all choices of the signs we computed all co-prime positive integer solutions $(x, y, a, b)$ satisfying the condition $\op{max}\{a, b\}\leq 50000$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On primitive integer solutions of the Diophantine equation $x^3\pm y^3=a^k\pm b^k$ Ulas, Maciej Number Theory In this note we consider the title Diophantine equation from both theoretical as well as experimental point of view. In particular, we prove that for $k=4, 6$ and each choice of the signs our equation has infinitely many co-prime positive integer solutions. For $k=5, 7$ and all choices of the signs we computed all co-prime positive integer solutions $(x, y, a, b)$ satisfying the condition $\op{max}\{a, b\}\leq 50000$. |
| title | On primitive integer solutions of the Diophantine equation $x^3\pm y^3=a^k\pm b^k$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.06567 |