항전 OJ - 1098 Ignatius's puzzle

Ignatius's puzzle


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

 
이 문제는 프로그래밍에 있지 않고 수학에 있다!수학 귀납법 증명!마지막으로 18+k*a가 65를 제거할 수 있다는 것을 증명하면 된다.
코드:
#include<stdio.h>

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

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

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