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Without the generalized Riemann hypothesis, there is no single value of a for which Artin's conjecture is proved. 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.
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 ...
Download as PDF; Printable version; In other projects ... Abc conjecture; Agoh–Giuga conjecture; Andrica's conjecture; Artin's conjecture on primitive roots; B ...
Download QR code; Print/export Download as PDF; Printable version; ... Artin's conjecture on primitive roots; B. Bateman–Horn conjecture; Birch's theorem; Bombieri ...
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
Psychologists Arthur and Elaine Aron are known for research behind the “36 Questions That Lead to Love.” They share how their relationship has lasted over 50 years.
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.