hdoj 5675 ztr loves math 【数学】

题目链接：hdoj 5675 ztr loves math

ztr loves math

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 201 Accepted Submission(s): 97

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=132−82

题意：问你n = x^2 - y^2有没有正整数解。

思路：显然就是两个完全平方数之间的距离，临近的距离为3、5、7、9…，可以连续相加，发现只有偶数可以分成两个不同的奇数(大于1)和也是合法的。

AC代码：

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cstring>
#define CLR(a, b) memset(a, (b), sizeof(a))
using namespace std;
typedef long long LL;
const int MAXN = 5*1e6 +10;
const int INF = 0x3f3f3f3f;
int main()
{
    int t; scanf("%d", &t);
    while(t--) {
        __int64 n; scanf("%I64d", &n);
        if(n == 1LL) {
            printf("False\n");
        }
        else if(n & 1LL) {
            printf("True\n");
        }
        else if((n / 2 - 1) & 1 && (n / 2 - 1) >= 3) {
            printf("True\n");
        }
        else {
            printf("False\n");
        }
    }
    return 0;
}