hdu 5675 ztr loves math（数学技巧）

Problem Description

ztr loves research Math.One day,He thought about the "Lower Edition" of triangle equation set.Such as n=x2−y2.

He wanted to know that ,for a given number n,is there a positive integer solutions?

Input

There are T test cases. 
The first line of input contains an positive integer T(T<=106) indicating the number of test cases.

For each test case:each line contains a positive integer ,n<=1018.

Output

If there be a positive integer solutions,print True,else print False
 

Sample Input

4
6
25
81
105

Sample Output

False
True
True
True

Hint

For the fourth case,$105 = 13^{2}-8^{2}$

 

给定nz，寻找是否存在一组(x,y)，满足x^2-y^2=n,那么我们可以构造两个方程 即（k+1）^2-k^2=n和（k+1）^2-(k-1)^2=n，得出结论，当n为奇数或者4的倍数时，方程一定有正整数解，但要记得特判1和4

 

AC代码：

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
#define ll long long
ll n;
int main()
{
    int t;
    scanf("%d",&t);
    while(t--){
       scanf("%I64d",&n);
       if(n==1 || n==4){
          printf("False
");
          continue;
       }
       if(n%2==1 || n%4==0){
           printf("True
");
       }else{
           printf("False
");
       }
    }
    return 0;
}