Solution to Project Euler Problem 9 - Finding Pythagorean triplets

http://projecteuler.net/problem=9

Problem: 

A Pythagorean triplet is a set of three natural numbers, a  b  c, for which,

a² + b² = c²

For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

Answer:

    (200*200) + (375*375)) == (425 * 425)

      40000 + 140625 = 180625

        200 + 375 + 425 = 1000

Solution:

#!/usr/bin/perl -w

use strict;

my ($a,$b,$c,$ulimit);

$ulimit=1000;

print "Pythogon triplets \n";

for ($a=1;$a<=$ulimit;$a++)   {

  for ($b=1;$b<=$ulimit;$b++ ) {

    if ($a < $b ) {

      for ($c=1; $c<=$ulimit;$c++) {

        if ( $b < $c ) {

          if ( (($a*$a) + ($b*$b)) == ($c * $c) ) {

            print "  ($a*$a) + ($b*$b)) == ($c * $c) \n";

            my $aa=$a*$a;

            my $bb=$b*$b;

            my $cc=$c*$c;

            print "    $aa + $bb = $cc \n";

            if ( ($a + $b + $c) == 1000 ) {

                print "FOUND: $a + $b + $c = 1000 \n";

                exit(0);

            }

          }

        }

       }

    }

  }

}