HDU1098——Ignatius's puzzle

Ignatius's puzzle

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3518    Accepted Submission(s): 2319

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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数学归纳法证明！ 最后只要证明 18 + k * x 能整除65就可以了。

 

#include<stdio.h>

 int main ()
 {
     int i = 0;
     int k = 0;

     while ( scanf ( "%d" , &k ) != EOF )
     {
           if ( k % 65 == 0 )
           {
                printf ( "no\n" ) ;
                continue ;
           }
           for ( i = 1 ; i <= 65 ; ++ i )
           {
               if ( ( 18 + k * i ) % 65 == 0 )
               {
                    printf ( "%d\n" , i ) ;
                    break ;
               }
           }
           if ( i > 65 )
           {
                printf ( "no\n" ) ;
           }
     }
     return 0 ;
 }