HDU 6051原根 + 欧拉函数

题解:

主要是原根的幂表示[1, p - 1],
然后转换
hint里的公式:
找了一篇证明:http://blog.youkuaiyun.com/Clove_unique/article/details/53152473

代码:

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;

const ll mod = 1e9 + 7;

ll m, p;

ll getPhi(ll x)
{
    ll ret = x;
    for(ll i = 2; i * i <= x; ++i)
    {
        if(x % i == 0)
        {
            while(x % i == 0) x /= i;
            ret -= ret / i;
        }
    }
    if(x > 1) ret -= ret / x;
    return ret;
}

ll get(int n, int fac)
{
    return (ll)fac * fac % mod * (((ll)n * getPhi(n) + (n == 1)) / 2) % mod;
}

int cal(int x)
{
    int ret = 0;
    for(int i = 1; (ll)i * i <= x; ++i)
    {
        if(x % i == 0)
        {
            ret = (ret + get(x / i, i)) % mod;
            if(i != x / i) ret = (ret + get(i, x / i)) % mod;
        }
    }
    ret -= ((ll)x * (x + 1) / 2) % mod;
    ret = (ret % mod + mod) % mod;
    return ret;
}

int main()
{

    int t;
    scanf("%d", &t);

    int kas = 0;
    while(t--)
    {
        scanf("%lld%lld", &m, &p);
        ll res = cal(p - 1);
        printf("Case #%d: %d\n", ++kas, (res * m) % mod);
    }

    return 0;
}