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,...
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, 1, and thus 3...
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, 1, and thus 3...
Description We say that integer 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 ...
Primitive Root¶ Definition¶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 ...
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...
Similar explicit bounds are also provided for the number of k-consecutive Lehmer numbers modulo a prime, and k-consecutive Lehmer primitive roots We also prove that for any prime number p>3.05×1014, there exists a Lehmer non-primitive root modulo p. Moreover, we show that for any ...
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, ...
You probably know that the primitive root modulo mm exists if and only if one of the following is true:m=2m=2 or m=4m=4; m=pkm=pk is a power of an odd prime number pp; m=2pkm=2pk is twice a power of an odd prime number pp.Today...
For example, we conjecture that for any odd prime $p$ there is a primitive root $g0$, and that for any prime $p>3$ there is a prime $q3$ there exists a Fibonacci number $F_k doi:10.48550/arXiv.1405.0290Sun, ZhiWeiMathematicsZ.-W. Sun, New observations on primitive roots modulo ...