URI routing in codeigniter

URI routing in codeigniter

As the title suggests, my issue is with codeIgniter.
I have used a code in an .htaccess file to remove index.php whcih works
all OK.
But I need to go further in changing the URI:
My main controller is page(), so when a user is in my homepage, the
URL-bar shows:
www.example.com/page/
(because homepage is index page, it does not show the page name as usual
the controller suffice),
but If I go to registration page, the URL-bar shows:
www.example.com/page/register
Up to here everything is OK, but I want the codeIgniter to show my domain
without the page() when the user is in my homepage, I don't want foolish
www.example.com/page/ to appear and I think when someone is visiting index
page, the URL-bar better to be www.example.com