（hdu1098）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  

题意：给定k，求最小的a满足f(x)=5*x^13+13*x^5+k*a*x，如果不存在就输出no

a满足f（x）则a满足f（x+1） ->  65|18 + ka ->  ka = 47（mod 65） 有解的情况 gcd（k,65）|47  -> gcd(k,65) == 1的时候有解

暴力求解；

#include <stdio.h> #include <string.h> int gcd(int a,int b) { return b ? gcd(b,a % b) : a; } int main() { int k; while(scanf("%d",&k)!=EOF) { if(gcd(k,65) == 1) { int i; for(i = 0; ;i++) { if(k * i % 65 == 47) { printf("%d/n",i); break; } } } else printf("no/n"); } return 0; }