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 { (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.
root modulo 7.
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
求原根的个数。当p有原根时，它有φ(φ(p))个原根。此题中p为奇素数，所以φ(p)=p-1，φ(φ(p))=φ(p-1)，问题转化为求欧拉函数。
代码如下：
#include<stdio.h>
int euler_phi(int p) {
int phi = p;
for (int i = 2; i * i <= p; i++) {
if (!(p % i)) {
phi = phi - phi / i;
while (!(p % i))
p /= i;
}
}
if (p > 1)
phi = phi - phi / p;
return phi;
}
int main(void) {
int p;
while (scanf("%d", &p) != EOF) {
printf("%d\n", euler_phi(p - 1));
}
return 0;
}