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".
The input contains several test cases. Each test case consists of a nonegative integer k, More details in the Sample Input.
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.
题目大意为:对于函数f(x)=5*x^13+13*x^5+k*a*x,输入任意一个数k,是否存在一个数a,对任意x都能使得f(x)能被65整除,如果存在这样一个数a,则输出,如果不存在,输出no。
解题思路:假如存在a满足条件,因为是任意x,就假设x=1,则f(x)为18+ak,则(18+ak)%65==0,就存在数a,a的取值范围就是1到65,由于是求最小的a,所以只要找到一个a,就输出,然后break。
注:其实在读懂题以后,这就是一个数学问题,开始我不知道怎么确定a的范围,在请教数学好的同学以后,由于除数是65,所以a的范围为1到65,如果是66的话就相当于轮了一个周期。在这些英文题中,会经常有这些关键词(黑体斜体),可以把它标记出来。
#include<stdio.h>
int main()
{
int n,a,k;
while(scanf("%d",&k)!=EOF)
{
for(a=;a<=;a++)
{
if((+a*k)%==)
{
printf("%d\n",a);
break;
}
}
if(a>=)
printf("no\n");
}
return;
}