### Abstract

Given a subgroup G of the multiplicative group of a finite field, we investigate the number of representations of an arbitrary field element as a sum of elements, one from each coset of G. When G is of small index, the theory of cyclotomy yields exact results. For all other G, we obtain good estimates. This paper formed a portion of the author's doctoral dissertation.

Original language | English |
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Pages (from-to) | 179-187 |

Number of pages | 9 |

Journal | Pacific Journal of Mathematics |

Volume | 82 |

Issue number | 1 |

Publication status | Published - 1979 |

Externally published | Yes |

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## Cite this

Myerson, G. (1979). A combinatorial problem in finite fields, i.

*Pacific Journal of Mathematics*,*82*(1), 179-187.