enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  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. Multiplicative group of integers modulo n - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_group_of...

    Integer multiplication respects the congruence classes, that is, a ≡ a' and b ≡ b' (mod n) implies ab ≡ a'b' (mod n). This implies that the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ ...

  4. Lehmer random number generator - Wikipedia

    en.wikipedia.org/wiki/Lehmer_random_number_generator

    where the modulus m is a prime number or a power of a prime number, the multiplier a is an element of high multiplicative order modulo m (e.g., a primitive root modulo n), and the seed X 0 is coprime to m. Other names are multiplicative linear congruential generator (MLCG) [2] and multiplicative congruential generator (MCG).

  5. 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]

  6. Multiplicative order - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_order

    The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or ...

  7. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    Primitive root modulo m: A number g is a primitive root modulo m if, for every integer a coprime to m, there is an integer k such that g k ≡ a (mod m). A primitive root modulo m exists if and only if m is equal to 2, 4, p k or 2p k, where p is an odd prime number and k is a positive integer.

  8. Canon arithmeticus - Wikipedia

    en.wikipedia.org/wiki/Canon_arithmeticus

    The Canon arithmeticus is a set of mathematical tables of indices and powers with respect to primitive roots for prime powers less than 1000, originally published by Carl Gustav Jacob Jacobi . The tables were at one time used for arithmetical calculations modulo prime powers, though like many mathematical tables they have now been replaced by ...

  9. Fermat number - Wikipedia

    en.wikipedia.org/wiki/Fermat_number

    The Fermat numbers satisfy the following recurrence relations: = + = + for n ≥ 1, = + = for n ≥ 2.Each of these relations can be proved by mathematical induction.From the second equation, we can deduce Goldbach's theorem (named after Christian Goldbach): no two Fermat numbers share a common integer factor greater than 1.