定义13.2 - 原根 Primitive Root 推论13.3 - 原根的判断 证明 练习1 定理13.4 推论13.5 例子 证明* 13.6例题(需要答案可以评论或者私信呀) 注:本文是针对NTU MH3210 Number Theory的学习笔记,主要内容为基础数论,内容不难,无需大学的数学知识也可以理解大部分。答主是一年前学的这门课,当时没有在知乎上做总结,...
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
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 < 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, 1, and thus 3 is a pri...
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 ...
On the least prime primitive root modulo a prime We derive a conditional formula for the natural density of prime numbers having its least prime primitive root equal to , and compare theoretical results w... A Paszkiewicz,A Schinzel - 《Mathematics of Computation》 被引量: 6发表: 2002年 Co...
From this it follows that the primitive exponents modulo 23 are 2, 6, 7, and 8. In this case we only needed to know one primitive root modulo 11 (and a number coprime to 10), because the others could then be generated by exponential iteration. However, this gives an unambiguous result...
For primes p , the multiplicative group of reduced residues modulo p is cyclic, with cyclic generators being referred to as primitive roots. Here we survey a few results and conjectures on this subject, and we discuss generalizations to arbitrary moduli. A primitive root to a modulus n is a...
cyclotomic polynomials and isomorphic copiesprimitive congruence root moduloSummary. We present a formalization of roots of unity, define cyclotomic polynomials and demonstrate the relationship between cyclotomic polynomials and unital polynomials.doi:10.1002/9781118336816.ch5Broderic ArnesonPiotr Rudnicki...
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, 1, and thus 3 is a pri...