HDU 5430 Reflect

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5430

Problem Description

We send a light from one point on a mirror material circle,it reflects N times and return the original point firstly.Your task is calcuate the number of schemes.

 

Input

First line contains a single integer T(T≤10) which denotes the number of test cases.

For each test case, there is an positive integer N(N≤106).

 

Output

For each case, output the answer.

 

Sample Input

1 4

 

Sample Output

4

若入射角为a，则圆心角为2a，由于刚好回到原点，则2a*（N+1）必须为2kπ，其中k可以为任意整数，不难发现，只要a和N+1是互质数即可满足要求，判断是否是互质数我们可以求他们的公约数，如果求不出公约数的话，那就说明它们互质了。代码如下：

#include<iostream>
using namespace std;
int fun(int i,int n){
	int temp;
	while(i!=0&&i!=1){
		temp=n%i;
		n=i;
		i=temp;
	}	
	return i;
}

int main()
{
	int T;
	cin>>T;
	while(T--){
		int n;
		cin>>n;
		int cnt=0;
		for(int i=1;i<=n;i++){
			if(fun(i,n+1)){
		//		cout<<"yes";
				cnt++;
			}
		//	else cout<<"no";
		}
		cout<<cnt<<endl;
	}
	return 0;
}