HDU 2685 I won't tell you this is about number theory

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2685

题意：求gcd(a^m - 1, a^n - 1) mod k

思路：gcd(a^m - 1, a^n - 1) = a^gcd(m, n) - 1

code：

#include <stdio.h>

int gcd(int a, int b)
{
    return !b ? a : gcd(b, a%b);
}

int mod_pow(int a, int x, int mod)
{
    int tmp = a;
    int ret = 1;
    while(x) {
        if (x & 1) {
            ret = ret * tmp % mod;
        }
        tmp = tmp * tmp % mod;
        x >>= 1;
    }

    return ret;
}

int main()
{
    int t, a, m, n, k;
    scanf("%d", &t);
    while (t--) {
        scanf("%d %d %d %d", &a, &m, &n, &k);
        int d = gcd(m, n);
        int ans = mod_pow(a, d, k);
        printf("%d
", (ans - 1 + k) % k); 
    }

    return 0;
}