On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911142338625536 |
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| author | Inagaki, Munenori Matsumura, Hideki Sawa, Masanori Uchida, Yukihiro |
| author_facet | Inagaki, Munenori Matsumura, Hideki Sawa, Masanori Uchida, Yukihiro |
| contents | We elucidate, for the first time, a novel group-theoretic structure that arises from certain solutions of the $n$-dimensional Prouhet--Tarry--Escott problem of degree $2$ and size $n$. We prove that the group is isomorphic to the orthogonal group for a certain quadratic form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem Inagaki, Munenori Matsumura, Hideki Sawa, Masanori Uchida, Yukihiro Number Theory 11D72, 11E12 (Primary) 05E99, 14G05 (Secondary) We elucidate, for the first time, a novel group-theoretic structure that arises from certain solutions of the $n$-dimensional Prouhet--Tarry--Escott problem of degree $2$ and size $n$. We prove that the group is isomorphic to the orthogonal group for a certain quadratic form. |
| title | On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem |
| topic | Number Theory 11D72, 11E12 (Primary) 05E99, 14G05 (Secondary) |
| url | https://arxiv.org/abs/2508.20733 |