fzu1759 Super A^B mod C 扩展欧拉定理降幂

扩展欧拉定理：

\[ a^x \equiv a^{x\mathrm{\ mod\ }\varphi(p) + x \geq \varphi(p) ? \varphi(p) : 0}(\mathrm{\ mod\ }p)\]

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
typedef long long ll;
ll aa, cc;
char bb[1000005];
ll getPhi(ll x){
    ll ans=x;
    for(ll i=2; i*i<=x; i++)
        if(x%i==0){
            ans -= ans / i;
            while(x%i==0)   x /= i;
        }
    if(x>1) ans -= ans / x;
    return ans;
}
ll ksm(ll a, ll b, ll c){
    ll re=1;
    while(b){
        if(b&1) re = (re * a) % c;
        a = (a * a) % c;
        b >>= 1;
    }
    return re;
}
int main(){
    while(scanf("%lld %s %lld", &aa, bb, &cc)!=EOF){
        ll phi=getPhi(cc);
        int len=strlen(bb);
        ll tmp=0;
        for(int i=0; i<len; i++){
            tmp = tmp * 10 + bb[i] - ‘0‘;
            if(tmp>=phi)    break;
        }
        if(tmp>=phi){
            tmp = 0;
            for(int i=0; i<len; i++)
                tmp = (tmp * 10 + bb[i] - ‘0‘) % phi;
            printf("%lld\n", ksm(aa, tmp+phi, cc));
        }
        else    printf("%lld\n", ksm(aa, tmp, cc));
    }
    return 0;
}

原文地址：https://www.cnblogs.com/poorpool/p/8137960.html