poj 1543 Perfect Cubes

Perfect Cubes

Time Limit: 1000MS
Memory Limit: 10000K

Total Submissions: 10540
Accepted: 5658

Description

For hundreds of years Fermat's Last Theorem, which stated simply that for n > 2 there exist no integers a, b, c > 1 such that a^n = b^n + c^n, has remained elusively unproven. (A recent proof is believed to be correct, though it is still undergoing scrutiny.) It is possible, however, to find integers greater than 1 that satisfy the "perfect cube" equation a^3 = b^3 + c^3 + d^3 (e.g. a quick calculation will show that the equation 12^3 = 6^3 + 8^3 + 10^3 is indeed true). This problem requires that you write a program to find all sets of numbers {a,b,c,d} which satisfy this equation for a <= N.

Input

One integer N (N <= 100).

Output

The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their a values). The values of b, c, and d should also be listed in non-decreasing order on the line itself. There do exist several values of a which can be produced from multiple distinct sets of b, c, and d triples. In these cases, the triples with the smaller b values should be listed first.

Sample Input

24

Sample Output

Cube = 6, Triple = (3,4,5)
Cube = 12, Triple = (6,8,10)
Cube = 18, Triple = (2,12,16)
Cube = 18, Triple = (9,12,15)
Cube = 19, Triple = (3,10,18)
Cube = 20, Triple = (7,14,17)
Cube = 24, Triple = (12,16,20)

 

  1: #include<iostream>

  2: using namespace std;

  3: int main()

  4: {

  5: 	int n,i,j,k,m;

  6: 	int cub[101];

  7: 	for(i=0;i<=100;i++)

  8: 		cub[i]=i*i*i;

  9: 	cin>>n;

 10: 	for(i=1;i<=n;i++)

 11: 	{

 12: 		for(j=2;j<=i-2;j++)

 13: 		{

 14: 			for(k=j+1;k<=i-1;k++)

 15: 			{

 16: 				for(m=k+1;m<=i;m++)

 17: 				{

 18: 					if(cub[i]==cub[j]+cub[k]+cub[m])

 19: 						cout<<"Cube = "<<i<<", Triple = ("<<j<<","<<k<<","<<m<<")"<<endl;

 20: 					if(cub[i]<cub[j]+cub[k]+cub[m])

 21: 						break;

 22: 				}

 23: 			}

 24: 		}

 25: 	}

 26: 	return 0;

 27: }

 28: