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

## TL;DR

This paper uncovers a new group-theoretic structure linked to specific solutions of the higher-dimensional Prouhet--Tarry--Escott problem, showing it is isomorphic to an orthogonal group for a quadratic form.

## Contribution

It introduces a novel group-theoretic framework for solutions of the n-dimensional Prouhet--Tarry--Escott problem of degree 2 and establishes its isomorphism to an orthogonal group.

## Key findings

- Identifies a new group structure from solutions of the problem.
- Proves the group is isomorphic to an orthogonal group.
- First to connect these solutions with a quadratic form group.

## 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.