【数学】A Cubic number and A Cubic Number

2019年2月16日 0条评论 942次阅读 0人点赞于衡

A cubic number is the result of using a whole number in a multiplication three times. For example, $3 \times 3 \times 3 = 27$ so $27$

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 $p$

p

is a difference of two cubic numbers.

InputThe first of input contains an integer $T (1 \leq T \leq 100)$ which is the total number of test cases.
For each test case, a line contains a prime number $p (2 \leq p \leq 10^{12})$ .OutputFor each test case, output 'YES' if given $p$

p

is a difference of two cubic numbers, or 'NO' if not.

Sample Input

Sample Output

NO
NO
NO
YES
NO
NO
NO
YES
NO
NO

题意：给一个质数，判断该质数是否为两立方数之差

首先x^3-y^3为一个质数则展开立方差公式后发现：x=y+1

带入化简，得3*y（y+1）+1

所以一个质数n要是两立方数之差。有n-1是3的倍数，且n-1是两相邻数之积

#include<iostream>
#include <climits>
#include <cstdio>
#include <algorithm>
#define LL long long
using namespace std;
int main()
{
  int T;
  scanf("%d", &T);
  while (T--)
  {
    LL n;
    scanf("%lld", &n);
    //P=3*（y+1）*y+1
    if ((n - 1) % 3)
    {
      printf("NO\n");
      continue;
    }
    LL x = (LL)sqrt((n - 1) / 3);

    if (x*(x + 1) == (n - 1) / 3)
      printf("YES\n");
    else
      printf("NO\n");
  }
  return 0;
}