In this chapter we reintroduce primitive roots, or primitive elements, of finite fields. The existence of primitive roots has many useful consequences, from making computations easier via the use of “logarithms,” to contributing to a theoretical understanding of finite fields. Most of the rest of the book builds on the availability of primitive roots. Chapters 23–27 are primarily devoted to primitive roots and applications to numbers; Chapters 28–30 return to polynomials and congruence classes modulo a polynomial.
KeywordsFinite Field Commutative Ring Primitive Element Primitive Root Congruence Class
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