hdu 1098 Ignatius's puzz

时间:2023-02-03 16:36:54

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=;i<=;i++)
{
if((+k*i)%==){printf("%d\n",i);break;}
}
if(i>)printf("no\n");
}
return ;
}