How to list authors of one category

I want to list all the authors that have written posts for a single category, and for each author link to go to a page with his/her profile and the posts they’ve written.

So far, I’m calling the category I want and the number of posts from that category and then displaying the list of authors. The problem is it shows duplicate authors. Is there a better way to do this? And if not, how can I just code it to avoid duplicates? Your help is unbelievably appreciated. Thanks in advance, Rebecca.

<?php query_posts(‘showposts=20&cat=3’); ?>
<?php while (have_posts()) : the_post(); ?>

<?php the_author_posts_link (); ?>

<div style=”clear:both”></div>
<?php endwhile;?>