in reply to
Triangle Numbers Revisited

`use strict;
use warnings;
my ($i, $j, $inum, $jnum, $left);
$| = 1; print "Enter the number to check : ";
my $inp = <STDIN>;
BING:
for ($i = tget($inp); $i; $i--) { # BUG ON THIS LINE - SEE BELOW FOR F
+IX
$inum = tmake($i);
$left = tget($inp - $inum - 1) + 1;
for ($j = 1; $j < $left; $j++) {
$jnum = tmake($j);
last BING if (tis($inp - $inum - $jnum));
}
}
print " Your triangles are : $inum $jnum "
. ($inp - $inum - $jnum) . "\n";
sub tget { return int(sqrt(1 + $_[0] * 2) - .5); }
sub tmake { return (.5 * $_[0] * ($_[0] + 1)); }
sub tis { my $n = shift; return ($n == tmake(tget($n))); }
`

This is blazingly fast with numbers even several orders of magnitude larger than 987654321, and requires almost no memory to run.