HDU 1098 Ignatius's puzzle

Ignatius's puzzle

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 5767    Accepted Submission(s): 3970

Problem Description

Ignatius is poor at math,he falls across a puzzle problem,so he has no choice but to appeal to Eddy. this problem describes that:f(x)=5*x^13+13*x^5+k*a*x,input a nonegative integer k(k<10000),to find the minimal nonegative integer a,make the arbitrary integer x ,65|f(x)if
no exists that a,then print "no".

 

Input

The input contains several test cases. Each test case consists of a nonegative integer k, More details in the Sample Input.

 

Output

The output contains a string "no",if you can't find a,or you should output a line contains the a.More details in the Sample Output.

 

Sample Input

111009999

 

Sample Output

22no43

此题应用费马小定理及中国剩余定理可以容易的得出如果存在a使得要求成立，则有：

a*k≡47（mod65）

所以得到此结论后便可遍历求出答案。

代码：

#include <iostream>using namespace std;#define N 65int main(){    int n,s,i;    while(cin>>n)    {        n=n%N;        s=5*8*8+13*2*2;//中国剩余定理求出同余方程的解        s=s%N;       // cout<<s<<" "<<n<<endl;        for(i=1;i<=N;i++)        {            if(i*n%65==s)            {                cout<<i<<endl;                break;            }        }        if(i>N)            cout<<"no"<<endl;    }    return 0;}