原根Primitive Root令U_n 为模n 的unit的集合。 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...
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 ...
ThePrimitiveRoot(n)command returns the smallestprimitive rootmodulon, if it exists. • ThePrimitiveRoot(n, greaterthan = m)command returns the smallest primitive root modulongreater thanm. • ThePrimitiveRoot(n, ith = i)command returns theith smallest primitive root modulon. ...
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, ...
x, 0 < x < p, is a primitive root modulo odd prime p if and only if the set { (xi mod 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, 1, and thus 3 is a primitive root modulo 7....
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
Proposition 1:The positive integer n is a primitive exponent modulo m if and only if both m and (m–1)/2 are primes and n is a primitive root modulo (m–1)/2. Proposition 2:If m and (m–1)/2 are primes, then the number of distinct primitive exponents modulo (m–1)/2 is ...
In this paper, we give an explicit upper bound on [Formula: see text], the least primitive root modulo [Formula: see text]. Since a primitive root modulo [Formula: see text] is not primitive modulo [Formula: see text] if and only if it belongs to the set of integers less than [...
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...