my $p = shift;
my %residues;
my %factors;
foreach my $x (2..$p) {
   my $mod = ($x*$x) % $p;
   if (exists $residues{$mod}) {
      $factors{$x-$residues{$mod}}++ if $p % ($x-$residues{$mod}) == 0;
      $factors{$x+$residues{$mod}}++ if $p % ($x+$residues{$mod}) == 0;
   }
   else {
      $residues{$mod} = $x;
   }
}
foreach (sort {$a <=> $b} keys %factors) {
   print "$p = $_*", $p/$_, "\n";
}

##</code><code>##

1021% factor.pl 54
54 = 2*27
54 = 6*9
54 = 18*3
54 = 54*1