### Abstract

In earlier papers, for "large" (but otherwise unspecified) subsets A, B of Z _{p} and for h(x) Z _{p} [x], Gyarmati studied the solvability of the equations a + b = h(x), resp. ab = h(x) with a A, b B, x Z _{p} , and for large subsets A, B, C, D of Z _{p} Sárközy showed the solvability of the equations a + b = cd, resp. ab + 1 = cd with a A, b B, c C, d D. In this series of papers equations of this type will be studied in finite fields. In particular, in Part I of the series we will prove the necessary character sum estimates of independent interest some of which generalize earlier results.

Original language | English |
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Pages (from-to) | 129-148 |

Number of pages | 20 |

Journal | Acta Mathematica Hungarica |

Volume | 118 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jan 1 2008 |

### Keywords

- Character sum
- Equation
- Finite field

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gyarmati, K., & Sárközy, A. (2008). Equations in finite fields with restricted solution sets. I (Character sums).

*Acta Mathematica Hungarica*,*118*(1-2), 129-148. https://doi.org/10.1007/s10474-007-6192-5