Perfect Cubes |

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 , 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
(e.g. a quick calculation
will show that the equation 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 .

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) Cube = 24, Triple = (12,16,20)

**Note:** The programmer will need to be concerned with an efficient
implementation. The official
time limit for this problem is 2 minutes, and it is indeed possible to
write a solution to this problem
which executes in under 2 minutes on a 33 MHz 80386 machine.
Due to the distributed nature of
the contest in this region, judges have been instructed to make
the official time limit at their site
the greater of 2 minutes or twice the time taken by the judge's
solution on the machine being used to judge this problem.