Ignatius's puzzle（数论）

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Ignatius's puzzle

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 6503    Accepted Submission(s): 4505

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

   
   
   
   

    
    
    
    11
100
9999
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    22
no
43
   
   
   
   

 

Author

eddy

 

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用数学归纳法证明，可以知道18+k*a能被65整除，则f[x]能被65整除

 

 

//数学归纳法，只要18+ka能被65整除就可以了 
#include<stdio.h>
int main()
{
    int k,a;
    int flag;
    while(scanf("%d",&k)!=EOF)
    {
        if(k%65==0)
          {printf("no\n");continue;}
        flag=0;
        for(a=0;a<66;a++)
        {
            if((18+k*a)%65==0)break;
        }
        if(a>=66)printf("no\n");
        else printf("%d\n",a);    
    } 
    return 0;   
}