题目

打个表发现当 n = 时答案为 p ，否则为 1 ，然后套板子。

#include <iostream>
#include <algorithm>
#include <vector>
#include <cstring>
#include <cmath>

using namespace std;

#define int long long
using i64 = long long;

const int N = 1000100;
const i64 inf = 1e18 + 1;
const int mod = 998244353;

int n, m, primes[N], cnt;
bool st[N];

void init(int n = 1000010) {
  for (int i = 2; i <= n; i++) {
    if (!st[i]) primes[cnt++] = i;
    for (int j = 0; j < cnt && primes[j] * i <= n; j++) {
      st[i * primes[j]] = true;    
      if (i % primes[j] == 0) break;
    }
  }
}

i64 sqrt(i64 x) {
  i64 l = 0, r = 1e9;
  while (l < r) {
    i64 mid = l + r + 1 >> 1;
    if (1ll * mid * mid <= x) l = mid;
    else r = mid - 1;
  }
  return l;
}

bool is_prime(i64 n) {
  if (n == 1) return 0;
  for (i64 i = 2; i <= n / i; i++)
  if (n % i == 0) return false;
  return 1;
}

long long quick_pow(long long x, long long p, long long mod) {  // 快速幂
  long long ans = 1;
  while (p) {
    if (p & 1) ans = (__int128)ans * x % mod;
    x = (__int128)x * x % mod;
    p >>= 1;
  }
  return ans;
}

bool Miller_Rabin(long long p) {  // 判断素数
  if (p < 2) return 0;
  if (p == 2) return 1;
  if (p == 3) return 1;
  long long d = p - 1, r = 0;
  while (!(d & 1)) ++r, d >>= 1;  // 将d处理为奇数
  for (long long k = 0; k < 10; ++k) {
    long long a = rand() % (p - 2) + 2;
    long long x = quick_pow(a, d, p);
    if (x == 1 || x == p - 1) continue;
    for (int i = 0; i < r - 1; ++i) {
      x = (__int128)x * x % p;
      if (x == p - 1) break;
    }
    if (x != p - 1) return 0;
  }
  return 1;
}

signed main() {
  init();
  int T;
  cin >> T;
  while (T--) {
    srand((unsigned)time(NULL));
    i64 n;
    cin >> n;
    if (n == 1) {
      std::cout << 1 << " ";
      continue;
    }
    if (Miller_Rabin(n)) {
      std::cout << n % mod << " ";
      continue;
    }
    i64 res = inf;
    i64 t = sqrt(n);
    if (t * t == n) {  
      if (is_prime(t)) {
        cout << t % mod << ' ';
        continue;
      }
    }
    for (int i = 0; i < cnt; i++) {
      i64 p = primes[i];
      if (n % p == 0) {
        i64 tmp = n;
        while (tmp % p == 0) tmp /= p;
        if (tmp == 1) res = p;
        else res = 1;
      }
    }
    if (res == inf) res = 1;
    cout << res % mod << ' ';
  }
  exit(0);
}