U_n中的一个元素a被称为模n的原根(Primitive Root),若\{a,a^2,...,a^{|U_n|}=1\}=U_n 同样对模p和模p^e的原根的存在性和寻找方式进行了讲解和证明 当然,我们仍然不满足于仅仅讨论这两种情况。毕竟素数虽然有很多特别的性质,但其整数中合数也非常重要。 本节,我们将原根推广到更普遍的情况——求...
In modular arithmetic, a number g is called a primitive root modulo n if every number coprime to n is congruent to a power of g modulo n . Mathematically, g is a primitive root modulo n if and only if for any integer a...
In modular arithmetic, a branch of number theory, a primitive root modulo n is any number g with the property that any number coprime to n is congruent to a power of g (mod n). That is, if g is a primitive root (mod n), then for every integer a that has gcd(a, n) = 1, ...
We say that integer x, 0 < x < n, is a primitive root modulo n if and only if the minimum positive integer y which makes xy= 1 (mod n) true is φ(n) .Here φ(n) is an arithmetic function that counts the totatives of n, that is, the positive integers less than or equal ...
3.In this paper,we have studied the asymptotic formula of a number theoretic function about the primitive roots modulo N,and given a more precise asymptotic formula.研究一个关于n原根的数论函数的渐近性质,给出了一个较为精确的渐近公式。 3)root cause根本原因 1.The methodology of root cause analys...
Primitive Roots Description We say that integer x, 0 < x < p, is a primitive root modulo odd prime p if and only if the set { (ximod p) | 1 <= i <= p-1 } is equal to { 1, ..., p-1 }. For example, the consecutive powers of 3 modulo 7 are 3, 2, 6, 4, 5, ...
In this paper,we have studied the asymptotic formula of a number theoretic function about theprimitive rootsmodulo N,and given a more precise asymptotic formula. 研究一个关于n原根的数论函数的渐近性质,给出了一个较为精确的渐近公式。 3) root cause ...
词汇primitive root 释义 Definition ofprimitive rootin English: primitive root noun Mathematics An integer g that is relatively prime to a given integer n and such that the least power to which g can be raised to yield unity modulo n is the totient of n. ...
A primitive root of a prime p is an integer g such that g (mod p) has multiplicative order p-1 (Ribenboim 1996, p. 22). More generally, if GCD(g,n)=1 (g and n are relatively prime) and g is of multiplicative order phi(n) modulo n where phi(n) is the toti
By Horie [4, Theorem 2], l [??] [h.sup.-.sub.n]/[h.sup.-.sub.n-1] for all n [greater than or equal to] 1 if l is a primitive root modulo [p.sup.2] and l is larger than an explicit but complicated constant depending on p. A note on the relative class number of the...