hdu 6216 A Cubic number and A Cubic Number

ゝ一纸荒年。 2022-06-08 07:06 254阅读 0赞

A Cubic number and A Cubic Number

Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 438 Accepted Submission(s): 237

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

  1. 10
  2. 2
  3. 3
  4. 5
  5. 7
  6. 11
  7. 13
  8. 17
  9. 19
  10. 23
  11. 29

Sample Output

  1. NO
  2. NO
  3. NO
  4. YES
  5. NO
  6. NO
  7. NO
  8. YES
  9. NO
  10. NO
  31.    题目大意：
  37.    题目的意思就是说，给你一个素数P，问是否有两个数的立方差等于p，如果有输出YES，没有输出NO；
  53.    题目解析：
  59.    由题目可以得到，由于a^3-b^3=(a-b)(a^2+b^2+ab) 所以（a-b）a-b只有等于1，a^3-b^3的差才会是素数，所以可以得到
  65.    （i+1）^3-i^3;
  81.    代码：
  87.     #include <cstdio>
  88. #include <iostream>
  89. using namespace std;
  90. int main()
  91. {
  92.     //freopen("in.txt","r",stdin);
  93.     int T;
  94.     cin>>T;
  95.     while(T--)
  96.     {
  97.        long long n;
  98.         cin>>n;
  99.         for(long long i=1;i<100000000;i++){
  100.            if((i+1)*(i+1)*(i+1)-i*i*i>n){
  101.                 cout<<"NO"<<endl;
  102.                 break;
  103.            }
  104.            if((i+1)*(i+1)*(i+1)-i*i*i==n){
  105.                 cout<<"YES"<<endl;
  106.                 break;
  107.            }
  108.         }
  109.     }
  110.     return 0;
  111. }

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