hdu6216 A Cubic number and A Cubic Number

A Cubic number and A Cubic Number

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 638    Accepted Submission(s): 319

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

102357111317192329

 

Sample Output

NONONOYESNONONOYESNONO

 

Source

2017 ACM/ICPC Asia Regional Qingdao Online 

k为素数，k为两立方数相减

将k分解因式，素数只能是1*本身的形式----------> k只能为相邻两个立方数的差

k=3b(b+1)-1

k-1=3b(b+1)

(k-1)/3=b(b+1)

筛选：3的倍数------->sqrt+floor  相邻两数之积

#include <iostream>#include <stdio.h>#include <math.h>using namespace std;int main(){int t;long long p;long long temp;long long g;scanf("%d",&t);while(t--){scanf("%lld",&p);if((p-1)%3!=0){printf("NO\n");continue;}temp=(p-1)/3;g=floor(sqrt(temp));if(g*(g+1)==temp){printf("YES\n");}else{printf("NO\n");}}return 0;}