题目链接

题意：求sqrt(sqrt(2) + sqrt(3)) ^ 2n MOD 1024

思路：

代码：

#include 
  
   
#include 
   
     #include 
    
      #include 
     
       #include 
      
        using namespace std; const int MOD = 1024; int n; struct mat { int s[2][2]; mat(int a = 0, int b = 0, int c = 0, int d = 0) { s[0][0] = a; s[0][1] = b; s[1][0] = c; s[1][1] = d; } mat operator * (const mat& c) { mat ans; sizeof(ans.s, 0, sizeof(ans.s)); for (int i = 0; i < 2; i++) for (int j = 0; j < 2; j++) for (int k = 0; k < 2; k++) ans.s[i][j] = (ans.s[i][j] + s[i][k] * c.s[k][j]) % MOD; return ans; } }tmp(5, 12, 2, 5); mat pow_mod(int k) { if (k == 1) return tmp; mat a = pow_mod(k / 2); mat ans = a * a; if (k % 2) ans = ans * tmp; return ans; } int main() { int cas; scanf("%d", &cas); while (cas--) { scanf("%d", &n); mat ans = pow_mod(n); printf("%d\n", (ans.s[0][0] * 2 - 1) % MOD); } return 0; }