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  2. Primitive root modulo n - Wikipedia

    en.wikipedia.org/wiki/Primitive_root_modulo_n

    In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which g k ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n.

  3. Dirichlet character - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_character

    In analytic number theory and related branches of mathematics, a complex-valued arithmetic function: is a Dirichlet character of modulus (where is a positive integer) if for all integers and : [1]

  4. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Hadwiger's theorem (geometry, measure theory) Helly's theorem (convex sets) Holditch's theorem (plane geometry) John ellipsoid ; Jung's theorem ; Kepler conjecture (discrete geometry) Kirchberger's theorem (discrete geometry) Krein–Milman theorem (mathematical analysis, discrete geometry) Minkowski's theorem (geometry of numbers)

  5. Primitive root - Wikipedia

    en.wikipedia.org/wiki/Primitive_root

    In mathematics, a primitive root may mean: Primitive root modulo n in modular arithmetic; Primitive nth root of unity amongst the solutions of z n = 1 in a field; See ...

  6. Artin's conjecture on primitive roots - Wikipedia

    en.wikipedia.org/wiki/Artin's_conjecture_on...

    In number theory, Artin's conjecture on primitive roots states that a given integer a that is neither a square number nor −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes. This conjectural density equals Artin's constant or a rational multiple thereof.

  7. Geometrical properties of polynomial roots - Wikipedia

    en.wikipedia.org/wiki/Geometrical_properties_of...

    The complex conjugate root theorem states that if the coefficients of a polynomial are real, then the non-real roots appear in pairs of the form (a + ib, a – ib).. It follows that the roots of a polynomial with real coefficients are mirror-symmetric with respect to the real axis.

  8. Cyclotomic field - Wikipedia

    en.wikipedia.org/wiki/Cyclotomic_field

    The torsion subgroup of Z[ζ n] × is the group of roots of unity in Q(ζ n), which was described in the previous item. Cyclotomic units form an explicit finite-index subgroup of Z[ζ n] ×. The Kronecker–Weber theorem states that every finite abelian extension of Q in C is contained in Q(ζ n) for some n.

  9. Cyclotomic polynomial - Wikipedia

    en.wikipedia.org/wiki/Cyclotomic_polynomial

    It may also be defined as the monic polynomial with integer coefficients that is the minimal polynomial over the field of the rational numbers of any primitive nth-root of unity (/ is an example of such a root). An important relation linking cyclotomic polynomials and primitive roots of unity is

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