A New Proof of the Prouhet-Tarry-Escott Problem

TL;DR

This paper introduces a novel proof for the Prouhet-Tarry-Escott problem by generalizing the product generating function of the Thue-Morse sequence, offering new insights into equal sum of powers sets.

Contribution

It provides a new proof and a generalized generating function approach for the classical Prouhet-Tarry-Escott problem, advancing theoretical understanding.

Findings

New proof of the Prouhet-Tarry-Escott problem

Generalization of the product generating function for Thue-Morse sequence

Enhanced theoretical framework for equal sum of powers sets

Abstract

The famous Prouhet-Tarry-Escott problem seeks collections of mutually disjoint sets of non-negative integers having equal sums of like powers. In this paper we present a new proof of the solution to this problem by deriving a generalization of the product generating function formula for the classical Prouhet-Thue-Morse sequence.