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：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 using namespace std;
 5 #define ll long long
 6 ll n;
 7 int main()
 8 {
 9     int t;
10     scanf("%d",&t);
11     while(t--){
12        scanf("%I64d",&n);
13        if(n==1 || n==4){
14           printf("False\n");
15           continue;
16        }
17        if(n%2==1 || n%4==0){
18            printf("True\n");
19        }else{
20            printf("False\n");
21        }
22     }
23     return 0;
24 }