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Equations in finite fields with restricted solution sets. II (Algebraic equations)

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Abstract

Generalizing earlier results, it is shown that if \( \mathcal{A}, \mathcal{B}, \mathcal{C}, \mathcal{D} \) are “large” subsets of a finite field F q , then the equations a + b = cd, resp. ab + 1 = cd can be solved with \( a \in \mathcal{A}, b \in \mathcal{B}, c \in \mathcal{C}, d \in \mathcal{D} \). 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.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, H-1053, Budapest, Reáltanoda u. 13-15., Hungary

    K. Gyarmati

  2. Department of Algebra and Number Theory, Eötvös Loránd University, H-1117, Budapest, Pázmány Péter sétány 1/C., Hungary

    A. Sárközy

Authors
  1. K. Gyarmati
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  2. A. Sárközy
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Correspondence to K. Gyarmati.

Additional information

Research partially supported by the Hungarian National Foundation for Scientific Research, Grants No. T 043623, T 043631 and T 049693.

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Gyarmati, K., Sárközy, A. Equations in finite fields with restricted solution sets. II (Algebraic equations). Acta Math Hung 119, 259–280 (2008). https://doi.org/10.1007/s10474-007-7035-0

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  • DOI: https://doi.org/10.1007/s10474-007-7035-0

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