A Cubic number and A Cubic Number

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 0    Accepted Submission(s): 0

Problem Description

A cubic number is the result of using a whole number in a multiplication three times. For example, 3×3×3=27 so 27 is a cubic number. The first few cubic numbers are 1,8,27,64 and 125. Given an prime number p. Check that if p is a difference of two cubic numbers.

 

 

Input

The first of input contains an integer T (1≤T≤100) which is the total number of test cases.
For each test case, a line contains a prime number p (2≤p≤1012).

 

 

Output

For each test case, output 'YES' if given p is a difference of two cubic numbers, or 'NO' if not.

 

 

Sample Input

10

2

3

5

7

11

13

17

19

23

29

 

 

Sample Output

NO

NO

NO

YES

NO

NO

NO

YES

NO

NO

题意：判断能不能找到a³-b³等于一个质数p。

思路：一开始想着打表的，但是提交代码的长度是有限制的，emmm...

有一个公式叫做立方差公式

· 

因为p是一个质数，所以（a-b）肯定等于一。所以只要判断另一个因子是不是等于p就行了，就把原来的立方转化成平方可以正常算了。

#include <cstdio>

#include <cstring>

#include <iostream>

#include <algorithm>

#include <cmath>

using namespace std;

 

int main()

{

    int n;

    scanf("%d",&n);

    while(n--)

    {

        long long num;

        scanf("%I64d",&num);

        int flag=0;

        for(long long i=0;i<=1000000;i++)

        {

            long long sum=i*i+(i+1)*(i+1)+i*(i+1);

            if(num==sum)

            {

                flag=1;

                break;

            }

        }

        if(flag==1)

            printf("YES\n");

        else

            printf("NO\n");

    }

    return 0;

}