hdu 1098 Ignatius's puzz

有关数论方面的题要仔细阅读，分析公式。

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

 

 

 

题目大意：方程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整出；输入a；

解题报告：假设存在这个数a ,因为对于任意x方程都成立，所以，当x=1时f(x)=18+ka;有因为f(x)能被65整出，这可得出f(x)=n*65;

即：18+ka=n*65;若该方程有整数解则说明假设成立。

所以,只要找到a,使得18+k*a能被65整除,也就解决了这个题目.

#include<iostream>
using namespace std;
int main()
{
    int k,i;
    while(scanf("%d",&k)!=EOF)
    {
        for(i=1;i<=10000;i++)
        {
            if((18+k*i)%65==0){printf("%d
",i);break;}
        }
        if(i>10000)printf("no
");
    }
    return 0;
}