Primitive Roots
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 1279 | Accepted: 629 |
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 is a primitive root modulo 7.
Write a program which given any odd prime 3 <= p < 65536 outputs the number of primitive roots modulo p.
Write a program which given any odd prime 3 <= p < 65536 outputs the number of primitive roots modulo p.
Input
Each line of the input contains an odd prime numbers p. Input is terminated by the end-of-file seperator.
Output
For each p, print a single number that gives the number of primitive roots in a single line.
Sample Input
23 31 79
Sample Output
10 8 24
Source
题意：p是奇素数,如果{xi%p | 1 <= i <= p - 1} = {1,2,...,p-1},则称x是p的原根.
给出一个p,问它的原根有多少个.
原根和指数 设h为一整数,n为正整数，(h，n)=1，适合h^l=1(mod n)的最小正整数l叫做h对模n的次数。如果l=φ(n)，此时h称为模n的原根。1773年，L.欧拉首先证明了素数p有原根存在。1785年，勒让德证明了;设，恰有φ(l)个模p互不同余的数对模p 的次数为l。