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 an+bn+cn, 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 a3=b3+c3+d3 (e.g. a quick calculation will show that the equation 123=63+83+103 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<=200.
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.
The first part of the output is shown here:
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)
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace Cubes
{
class Program
{
static void Main(string[] args)
{
for (int i = 6; i < 200; i++)
{
for (int j = 2; j < 200; j++)
{
for (int k = j + 1; k < 200; k++)
{
for (int l = k + 1; l < 200; l++)
{
if ((i*i*i) == (j*j*j) + (k*k*k) + (l*l*l))
{
Console.WriteLine(i +" "+ j +" "+ k +" "+ l);
}
}
}
}
}
}
}
}
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