Newton polygons and the Prouhet-Tarry-Escott problem
type: Item
instance of: scholarly article
title: Newton polygons and the Prouhet-Tarry-Escott problem
zbMATH Open document ID: 1396.11057
author: Michael Filaseta
author: Maria Markovich
published in: Journal of Number Theory
publication date: 2017-01-23T00:00:00Z
review text: For \(n\geq 2\), the Prouhet-Tarry-Escott (PTE) problem asks for two lists of integers \(X=[x_1,\dots,x_n]\) and \(Y=[y_1,\dots,y_n]\) satisfying \(\sum_{i=1}^n x_i^e=\sum_{i=1}^n y_i^e\) for \(e\in\{1,\dots,k\}\), where \(k\) is an integer in the interval \([2,n-1]\). The authors use Newton polygons to obtain new information on the \(2\)-adic valuation of a certain constant associated with the PTE problem. Further, they give two explicit examples involving the cases \(n=8\) and \(n=9\).
reviewed by: Lajos Hajdu
Mathematics Subject Classification ID: 11D72
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 6676823
zbMATH Keywords: Newton polygons
zbMATH Keywords: Prouhet-Tarry-Escott problem
zbMATH Keywords: p-adic
MaRDI profile type: Publication
full work available at URL: j.jnt.2016.10.009
OpenAlex ID: W2558132777
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DOI: 10.1016/J.JNT.2016.10.009
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description: scientific article; zbMATH DE number 6676823