From your description I take you want (w, x, y, z) such that 0 <= z < y < x < w <= 100 and not w-x == x-y == y-z. In order to achieve this I would parametrize the loops using the differences dwx = w-x, dxy = x-y, dyz = y-z.

use strict;
use warnings;

my $n = 5; # should be 100
my $c1 = my $c2 = 0;
for my $w (3..$n) {
    for my $dwx (1..$w-2) {
        my $x = $w - $dwx;
        for my $dxy (1..$x-1) {
            my $y = $x - $dxy;
            for my $dyz (1..$y) {
                my $z = $y - $dyz;
                $c1++;
                next unless $dwx != $dxy or $dxy != $dyz;
                $c2++;
                print "$w $x $y $z\n";
            }
        }
    }
}
print "Found $c2 out of $c1 combinations\n";
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UPDATE: Changes next unless... for better readibility.