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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.

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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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Authors and Affiliations

  1. Instituto de Telecomunicações, Delegação da Covilhã, Department of Mathematics, Beira Interior University, Covilhã, Portugal

    C. Miguel

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  1. C. Miguel
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Correspondence to C. Miguel.

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Communicated by A. Constantin.

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Miguel, C. On the sumsets of exceptional units in a finite commutative ring. Monatsh Math 186, 315–320 (2018). https://doi.org/10.1007/s00605-017-1070-x

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  • DOI: https://doi.org/10.1007/s00605-017-1070-x

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