原题链接：http://acm.hdu.edu.cn/showproblem.php?pid=1098
| 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 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 |
注：65|f(x)是f(x)能被65整除。
此题属于数论里面的费马小定理：
是数论中的一个重要定理，其内容为：
假如p是质数，且gcd(a,p)=1，那么 a(p-1)≡1（mod p）。即：假如a是整数，p是质数，且a,p互质(即两者只有一个公约数1)，那么a的(p-1)次方除以p的余数恒等于1。
a^(p-1)%p=1
(其中%为取模操作，且a<p，p为质数)
#include <stdio.h>
#include <stdlib.h>
#include <string.h>int main()
{int k;while(~scanf("%d", &k)){int i;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;
}