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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.
Gauss proved [10] that for any prime number p (with the sole exception of p = 3), the product of its primitive roots is congruent to 1 modulo p. He also proved [11] that for any prime number p, the sum of its primitive roots is congruent to μ (p − 1) modulo p, where μ is the Möbius function. For example,
Artin's conjecture on primitive roots; The (now proved) conjecture that finite fields are quasi-algebraically closed; see Chevalley–Warning theorem; The (now disproved) conjecture that any algebraic form over the p-adics of degree d in more than d 2 variables represents zero: that is, that all p-adic fields are C 2; see Ax–Kochen theorem or ...
Artin conjecture (L-functions) number theory: Emil Artin: 650 Artin's conjecture on primitive roots: number theory: ⇐generalized Riemann hypothesis [2] ⇐Selberg conjecture B [3] Emil Artin: 325 Bateman–Horn conjecture: number theory: Paul T. Bateman and Roger Horn: 245 Baum–Connes conjecture: operator K-theory: ⇒Gromov-Lawson ...
This sequence is the set of primes p such that 10 is a primitive root modulo p. Artin's conjecture on primitive roots is that this sequence contains 37.395...% of the primes. Binary full reptend primes
Ninety-five million people across the northern U.S. from the plains to the Great Lakes as well as the Northeast are under winter weather alerts on Saturday as a blast of winter weather could foul ...
Artin's conjecture on primitive roots; B. ... Second Hardy–Littlewood conjecture; Sister Beiter conjecture; T. Twin prime conjecture; W. Waring–Goldbach problem;
Due to the book's commercial success and timeliness of the 2016 election, some tried to use "Hillbilly Elegy" to explain how Trump won over previously Democratic areas. This gave Vance the ...
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