the simplest way is to use uniq (see 'man uniq')

If you really want to do this in Perl or if this is really
your homework *grin* then:

#assuming that your file has only one email address per line
my %emails = ();
open FH, "<emails.dat" or die "error: $!";
$emails{$_}++ while (<FH>);
close FH;

open FH, ">new_emails.dat" or die "error: $!";
print FH $_ while ($_ = each(%emails));
close FH;
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--perlplexer