The fourth known primitive solution to $a^5 + b^5 + c^5 + d^5 = e^5$
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908981761409024 |
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| author | Braun, Jeffrey |
| author_facet | Braun, Jeffrey |
| contents | We report the fourth known primitive solution to the Diophantine equation $a^5 + b^5 + c^5 + d^5 = e^5$, extending the list of solutions from 1966, 1996, and 2004. This result was obtained via a large-scale computational search based on an optimized meet-in-the-middle strategy. We describe the search algorithm, the techniques enabling it at scale, and the computational ranges explored. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The fourth known primitive solution to $a^5 + b^5 + c^5 + d^5 = e^5$ Braun, Jeffrey Number Theory 11D41 (Primary) 11Y50 (Secondary) We report the fourth known primitive solution to the Diophantine equation $a^5 + b^5 + c^5 + d^5 = e^5$, extending the list of solutions from 1966, 1996, and 2004. This result was obtained via a large-scale computational search based on an optimized meet-in-the-middle strategy. We describe the search algorithm, the techniques enabling it at scale, and the computational ranges explored. |
| title | The fourth known primitive solution to $a^5 + b^5 + c^5 + d^5 = e^5$ |
| topic | Number Theory 11D41 (Primary) 11Y50 (Secondary) |
| url | https://arxiv.org/abs/2603.05549 |