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

Carsten Dietzel

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arXiv · 1309.7506

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

Carsten Dietzel

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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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Carsten Dietzel. 2013-09-28. A generalization of Schur's theorem and its application to consecutive power residues. https://arxiv.org/abs/1309.7506

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