URAL 1268. Little Chu 求最大原根

题目来源：URAL 1268. Little Chu

题意：输入n 求一个最大的k 使得k^1 k^2 k^3...k^x mod n 后各不相同

思路：mod n 后各不相同 最多有 n个 那么此事k就是原根 因为k <= n 所以从n开始向下枚举 求一个最大的原根

#include <cstdio>#include <cstring>using namespace std;typedef long long LL;int p[100000], c;LL pow_mod(LL a, LL x, LL m){LL ans = 1;while(x){if(x&1)ans = ans * a % m;a = a * a % m;x >>= 1;}return ans;}bool ok(int x, int ph, int m){for(int i = 0; i < c; i++)if(pow_mod(x, ph/p[i], m) == 1)return false;return true;}void divide(int x){c = 0;for(int i = 2; i*i <= x; i++){if(x % i == 0){p[c++] = i;while(x % i == 0)x /= i;}}if(x > 1)p[c++] = x;}int main(){int T;scanf("%d", &T);while(T--){int n;scanf("%d", &n);int m = n, ans = m;for(int i = 2; i*i <= n; i++){if(n%i == 0){ans = ans / i * (i-1);while(n%i == 0)n /= i;}}if(n > 1)ans = ans / n * (n-1);//printf("%d\n", ans);divide(ans);int x = ans;while(!ok(x, ans, m))x--;printf("%d\n", x);}return 0;}