### Abstract

Generalizing earlier results, it is shown that if A, B, C, D are "large" subsets of a finite field F _{q} , then the equations a + b = cd, resp. ab + 1 = cd can be solved with a ∈ A, b ∈ B, c ∈ C, d ∈ D. Other algebraic equations with solutions restricted to "large" subsets of F _{q} are also studied. The proofs are based on character sum estimates proved in Part I of the paper.

Original language | English |
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Pages (from-to) | 259-280 |

Number of pages | 22 |

Journal | Acta Mathematica Hungarica |

Volume | 119 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 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. II (Algebraic equations).

*Acta Mathematica Hungarica*,*119*(3), 259-280. https://doi.org/10.1007/s10474-007-7035-0