2017青岛赛区亚洲区域赛网络赛 1011题题解

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

思路：若能找到一个整数n满足 p=3n²+3n+1 则为YES（好不容易找到的规律）

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <cmath>
#include <algorithm>
#include <vector>
#include <map>
#include <string>
#include <stack>
#define LL long long
#define INF 0x7fffffff
#define MAX 200010
#define PI 3.1415926535897932
#define E 2.718281828459045
using namespace std;
int t;
LL p;
int main()
{
scanf("%d",&t);
while(t--){
scanf("%lld",&p);
bool flag=false;
p=p-1;
if(p%3==0){
p=p/3;
LL n=(LL)sqrt(1.0*p);
if(n*n+n==p) flag=true;
}
if(flag)printf("YES\n");
else printf("NO\n");
}
return 0;
}