On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem

Munenori Inagaki; Hideki Matsumura; Masanori Sawa; Yukihiro Uchida

On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem

Number Theory 2025-09-09 v2

Authors: Munenori Inagaki , Hideki Matsumura , Masanori Sawa , Yukihiro Uchida

Abstract

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.

Keywords

Prouhet--Tarry--Escott problem group structure orthogonal group quadratic form normalized solutions

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@article{arxiv.2508.20733,
  title  = {On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem},
  author = {Munenori Inagaki and Hideki Matsumura and Masanori Sawa and Yukihiro Uchida},
  journal= {arXiv preprint arXiv:2508.20733},
  year   = {2025}
}

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5 pages

On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem

Abstract

Keywords

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