Ignatius's puzzle

Ignatius's puzzle

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4935    Accepted Submission(s): 3359

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

 

若对任意x成立,则当x=1时必然成立.若当x=1时成立,则对任意正整数x都成立.

观察题目中给出的式子可以看出每一项都有公因子x,所以f(x)必然是f(1)的x倍,若f(1)是65的倍数,则f(x)必然也是65的倍数.

#include<stdio.h>
int main()
{
    int k;
    while (scanf("%d",&k)!=EOF)
    {
        if (k==1 || (k%5!=0 && k%13!=0 && k%65!=0))
        {
            for (int i=1;;i++)
            if ((18+k*i)%65==0)
            {
                printf("%d\n",i);
                break;
            }
        }
        else printf("no\n");
    }
    return 0;
}