hdu-1098 Ignatius's puzzle

(数学归纳法证明)

Ignatius's puzzle

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 5511    Accepted Submission(s): 3773

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
   
   
   
   

 

题目大意：f(x)=5*x^13+13*x^5+k*a*x   现输入一个k，看是否存在a 使得对任意的x都满足65|f(x).

解题思路：既然对任意的x满足，则当x=1时也满足。f(1)=(18+K*a)  ------->  (18+k*a)%65==0   又因为当a>65时，可以看成是  a=65+b 。所以只需要在1~65之间寻找a 就行

#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<iostream>
#include<algorithm>
using namespace std;
int main()
{
    int k,a,i,j;
    while(~scanf("%d",&k))
    {
        i=0;
        for(j=1;j<=65;j++)
        {
            if((18+k*j)%65==0)
            {
                i=1;
                break;
            }
        }
        if(i)
            printf("%d\n",j);
        else
            printf("no\n");
    }
    return 0;
}