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  2. Primitive root modulo n - Wikipedia

    en.wikipedia.org/wiki/Primitive_root_modulo_n

    If g is a primitive root modulo p, then g is also a primitive root modulo all powers p k unless g p −1 ≡ 1 (mod p 2); in that case, g + p is. [14] If g is a primitive root modulo p k, then g is also a primitive root modulo all smaller powers of p. If g is a primitive root modulo p k, then either g or g + p k (whichever one is odd) is a ...

  3. 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.

  4. Möbius function - Wikipedia

    en.wikipedia.org/wiki/Möbius_function

    Publication year: 1832: ... Another characterization by Gauss is the sum of all primitive roots. [4] Values. The values of ... 20 −1 0 −1 1 1 0 ...

  5. Artin's conjecture on primitive roots - Wikipedia

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

    D. R. Heath-Brown proved in 1986 (Corollary 1) that at least one of 2, 3, or 5 is a primitive root modulo infinitely many primes p. [3] He also proved (Corollary 2) that there are at most two primes for which Artin's conjecture fails.

  6. Dirichlet character - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_character

    The principal character is not primitive. [34] The character , =,,... is primitive if and only if each of the factors is primitive. [35] Primitive characters often simplify (or make possible) formulas in the theories of L-functions [36] and modular forms.

  7. Donald Trump Is TIME's 2024 Person of the Year - AOL

    www.aol.com/donald-trump-times-2024-person...

    Already, he has floated 25% tariffs on Mexico and Canada, a move that most economists predict will cause prices to rise. And he plans to increase tariffs on Chinese imports, aiming to coerce ...

  8. Carmichael function - Wikipedia

    en.wikipedia.org/wiki/Carmichael_function

    There are four primitive λ-roots modulo 15, namely 2, 7, 8, and 13 as . The roots 2 and 8 are congruent to powers of each other and the roots 7 and 13 are congruent to powers of each other, but neither 7 nor 13 is congruent to a power of 2 or 8 and vice versa.

  9. Trump demands immediate dismissal of New York "hush money ...

    www.aol.com/trump-demands-immediate-dismissal...

    Former President Donald Trump and his attorney Todd Blanche exit the courthouse and speak to media after Trump was found guilty following his hush money trial at Manhattan Criminal Court on May 30 ...