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

Munenori Inagaki; Hideki Matsumura; Masanori Sawa; Yukihiro Uchida

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arXiv · 2508.20733

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

Munenori Inagaki·Hideki Matsumura·Masanori Sawa·Yukihiro Uchida

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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.

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Munenori Inagaki, Hideki Matsumura, Masanori Sawa, Yukihiro Uchida. 2025-08-28. On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem. https://arxiv.org/abs/2508.20733

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