If a G is an element of maximal order in G, then the order of every element of G is a divisor of the order of a. 6.5.10. The multiplicative group of nonzero elements of a finite field is cyclic. Any finite field is a simple extension of its prime subfield. Irreducible polynomials over finite fields 6.6.1. Theorem. R be a multiplicative function.
R be any function.
R be any function. Quadratic reciprocity 6.7.1. The symbol is called the Legendre symbol . If p is an odd prime, and if a Z with p a, then 6.7.3. Theorem. Let p be an odd prime.