Web29 de abr. de 2013 · 1 Answer. Sorted by: 3. Trivially, any upper bound for the least prime quadratic residue modulo p is also an upper bound for the least prime non-primitive … Web11 de abr. de 2024 · Abstract. Let p>3 be a prime number, \zeta be a primitive p -th root of unity. Suppose that the Kummer-Vandiver conjecture holds for p , i.e., that p does not …

ON THE LEAST PRIMITIVE ROOT OF A PRIME

Web21 de jan. de 2024 · We will introduce an indicator function for primitive roots of primes in §2.1 and together with results from §1.2.1, §1.2.3 and §1.2.4 we will outline the first step … Web10 de abr. de 2024 · This note considers a few estimates of the least primitive roots g(p) and the least prime primitive roots g^*(p) of cyclic groups G of order #G = p - 1 associated with the integers modulo p. pope marked you

Contents 1 The Primitive Root Theorem

Web10 de abr. de 2024 · Under GRH, the distribution of primes in a prescribed arithmetic progression for which g is primitive root modulo p is also studied in the literature (see, [ 8, 10, 12 ]). On the other hand, for a prime p, if an integer g generates a subgroup of index t in ( {\mathbb {Z}}/p {\mathbb {Z}})^ {*}, then we say that g is a t -near primitive root ... WebIn 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.So g is a primitive … WebTheorem 1.1. If pis a positive prime, then there is at least one primitive root bamong the units of Z=pZ. Proofs of Theorem 1.1 typically involve proving the following results: Let pbe prime. If f(x) is polynomial with coe cients in Z=pZ, of degree d, then at most dcongruence classes modulo pare roots of f. If a;bare units in Z=pZ such that gcd(ord sharepoint 権限 確認