hdu 2866 Special Prime（数论，推公式）

Special Prime

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 390    Accepted Submission(s): 200

Problem Description

Give you a prime number p, if you could find some natural number (0 is not inclusive) n and m, satisfy the following expression: 
  
We call this p a “Special Prime”.
AekdyCoin want you to tell him the number of the “Special Prime” that no larger than L.
For example:
  If L =20
1^3 + 7*1^2 = 2^3
8^3 + 19*8^2 = 12^3
That is to say the prime number 7, 19 are two “Special Primes”.

 

Input

The input consists of several test cases.
Every case has only one integer indicating L.(1<=L<=10^6)

 

Output

For each case, you should output a single line indicate the number of “Special Prime” that no larger than L. If you can’t find such “Special Prime”, just output “No Special Prime!”

 

Sample Input

7 777

 

Sample Output

1 10

Hint

思路参考： 点击打开链接

这里有个疑问，为什么把n=x³，n+p=y³需要先证明gcd（n²，n+p）=1？

代码：

#include 
#include 
#include 
#include 
#include 
using namespace std;
#define N 1000001
#define LL long long
int prime[N],notprime[N];
void init()
{
    for(int i=2;i*in) break;
            if(!notprime[tmp])
                num++;
        }
        if(!num) printf("No Special Prime!\n");
        else printf("%d\n",num);
    }
    return 0;
}