Program correctly factors 24 to 4*6 and 2*12 but misses 3*8. Program finds no factors for 54.

YuckFoo

Update: With a little thought one can see the program will only find factor pairs that are both even or both odd. x+y * x-y = p.

#!/usr/bin/perl

   use strict;

   my ($num) = @ARGV;

   my $x = int(sqrt($num)) + 1;
   my $y = sqrt($x * $x - $num);

   while ($x - $y >= 2) {

      if ($y == sprintf("%d", $y)) {
         print "Ok $num = ", $x-$y, " * ", $y+$x, "\n";
      }
      else { print "No x = $x, y = $y\n"; }

      $x++;
      $y = sqrt($x * $x - $num);
   }
[download]