FZU 1759 题解 欧拉降幂

本题考点：欧拉降幂

Super A^B mod C

Given A,B,C, You should quickly calculate the result of A^B mod C. (1<=A,C<=1000000000,1<=B<=10^1000000).

Input

There are multiply testcases. Each testcase, there is one line contains three integers A, B and C, separated by a single space.

Output

For each testcase, output an integer, denotes the result of A^B mod C.

Sample Input

3 2 4

2 10 1000

Sample Output

1

23

分析：欧拉降幂的模板题

直接套公式即可：

AC代码:

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
typedef long long ll;
ll a,p;
char b[10000005];
ll phi(ll x)
{
    ll res=x;
    ll a=x;
    for(int i=2;i*i<=x;i++)
    {
        if(a%i==0)
        {
            res=res/i*(i-1);
            while(a%i==0)    a/=i;
        }
    }
    if(a>1)    res=res/a*(a-1);
    return res;
}
ll qp(ll a,ll b,ll p)
{
    ll ans=1;
    while(b)
    {
        if(b&1)
        {
            ans=(ans*a)%p;
        }
        a=(a*a)%p;
        b>>=1;
    }
    return ans;
}
int main()
{
    //freopen("input.txt","r",stdin);
    while(scanf("%lld %s %lld",&a,&b,&p)!=EOF)
    {
        ll len=strlen(b);
        ll res=0;
        ll pp=phi(p);
        for(int i=0;i<len;i++)
        {
            res=(res*10+b[i]-‘0‘)%pp;
        }
        printf("%lld\n",qp(a,res,p));
    }
    return 0;
}

原文地址：https://www.cnblogs.com/cautx/p/11396842.html