A link (not in the post) to download a specific PDF file

The pdf is itself an attachment post so in wordpress template hierarchy we can create a template named pdf.php Then you can write following code in it which force download the pdf file.

<?php  

if (have_posts()) :
the_post();

$pdf_title = $post->post_title;
$pdf_src = get_attached_file($post->ID );
$bytes =  filesize( $pdf_src );

 header("Pragma: public"); // required
 header("Expires: 0");
 header("Cache-Control: must-revalidate, post-check=0, pre-check=0");
 header("Cache-Control: private",false); // required for certain browsers 
 header("Content-Type: application/pdf");
 header("Content-Disposition: attachment; filename=\"".$pdf_title."\";" );
 header("Content-Transfer-Encoding: binary");
 header("Content-Length: ".$bytes);
 ob_clean();
 flush();
 readfile("$pdf_src");


endif;

While linking the button link to its attachment page( not the file url) and the job will be done. Good luck.