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eulerphi.cc
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eulerphi.cc
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/*
* Euler's Phi function:
*
* Author: Ethan Kim
* Complexity: O(sqrt(n))
*
* Computes Euler's Phi(Totient) function; Given a positive n, computes
* the number of positive integers that are <= n and relatively prime to n.
*
* For prime n, it is easy to see that phi(n)=n-1.
* For powers of prime, phi(p^k)=p^(k-1) * (p-1).
* Also, phi is multiplicative, so phi(pq)=phi(p)*phi(q), if p and q are
* relatively prime.
*
*/
#include <iostream>
#include <cassert>
using namespace std;
int fast_exp(int b, int n)
{
int res = 1;
int x = b;
while (n > 0) {
if (n & 0x01) {
n--;
res *= x;
} else {
n >>= 1;
x *= x;
}
}
return res;
}
int phi(int n) {
int k, res;
long long p;
assert(n > 0);
res=1;
for(k = 0; n % 2 == 0; k++) {
n /= 2;
}
if (k)
res *= fast_exp(2, k-1);
for (p = 3; p*p <= n; p += 2) {
for (k = 0; n % p == 0; k++) {
n /= p;
}
if (k) {
res *= fast_exp(p, k-1) * (p-1);
}
}
if (n > 1) {
res *= n-1;
}
return res;
}
int main(void) {
int p;
while(cin >> p && p) {
cout << phi(p) << endl;
}
return 0;
}