Ignatius's puzzle（数论）

链接：点击打开链接

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

 

Recommend

We have carefully selected several similar problems for you:   1097  1082  1064  1124  1164 

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;   
}