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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.
If is a primitive root modulo the prime , then (). Artin's conjecture on primitive roots states that a given integer a that is neither a perfect square nor −1 is a primitive root modulo infinitely many primes.
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 ...
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
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 ...
Artin's conjecture on primitive roots; B. Bateman–Horn conjecture; Birch's theorem; Bombieri norm; Brauer–Siegel theorem; Brun's constant; Buchstab function; C.
Artin's conjecture on primitive roots; B. Balanced prime; Bateman–Horn conjecture; Beal conjecture; Birch and Swinnerton-Dyer conjecture; Brocard's conjecture;
Primitive root modulo n. ... Artin conjecture; Sato–Tate conjecture; Langlands program; modularity theorem; ... Integer square root; Algebraic number.