A generalization of Schur's theorem and its application to consecutive power residues

2013/09/28 by Carsten Dietzel, Dietzel, Carsten
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1309.7506

5 pages

arxiv created 2013/09/28 · arxiv updated 2013/10/01

Abstract

This article provides a proof of a generalization of Schur's theorem on the partition regularity of the equation x+y=z, which involves a divisibility condition. This generalization will be utilized to prove the existence of 'small' consecutive power residues modulo p, where p is a sufficiently large prime.

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