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Equations over Finite Fields

  • J. S. Chahal
Part of the The University Series in Mathematics book series (USMA)

Abstract

We have seen that for each prime p, there is a field F p of p elements. In fact, given any prime p and an integer r ≥ 1, there is one and only one field F q of q = p r elements. The field F q ⊇ F p and for each α in F q , pα = 0. Conversely, any finite field is F q , for some q = p r (cf. Ref. 18). The field F q is characterized by the property
$$f\left( X \right) = X^q - X = \mathop \Pi \limits_{\alpha \varepsilon {\text{F}}_q } \;\left( {X - \alpha } \right)$$
.

Keywords

Zeta Function Modular Form Elliptic Curve Finite Field Elliptic Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • J. S. Chahal
    • 1
  1. 1.Brigham Young UniversityProvoUSA

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