On the sumsets of exceptional units in a finite commutative ring

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Abstract

Let R be a finite commutative ring with identity. In this paper, given an integer \(k\ge 2\), we obtain an exact formula for the number of ways to represent each element of R as the sum of k exceptional units. This generalizes a recent result of Quan-Hui Yang and Qing-Qing Zhao for the case where R is the ring \({\mathbb {Z}}_n\) of residue classes modulo n.

Keywords

Exceptional unit Finite field Finite ring 

Mathematics Subject Classification

11B13 11L05 11T24 

Notes

Acknowledgements

The author expresses his gratitude to the anonymous reviewer for his/her helpful comments and suggestions, which have improved the paper.

This work was supported by FCT project UID/EEA/50008/2013.

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Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.Instituto de Telecomunicações, Delegação da Covilhã, Department of MathematicsBeira Interior UniversityCovilhãPortugal

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