You forgot to add RewriteBase. Without it, you are redirected to the address /home/USER/public_html/article.php etc.
\r
Do this:
\r
RewriteEngine on
RewriteBase /
RewriteRule ^article/([0-9]+) article.php?id=$1 [L]
\r
\r
Well, for your needs a rule adjust (given other parameters). To check how are redirects, temporarily put R instead of L
