Testing for paginated Pages

I found these two examples:

“You can use this code to check whether you’re on the nth page in a Post or PAGE Page that has been divided into pages using the <!–nextpage–> QuickTag. This can be useful, for example, if you wish to display meta-data only on the first page of a post divided into several pages.”

<?php
$paged = $wp_query->get( 'paged' );

if ( ! $paged || $paged < 2 )
{
    // This is not a paginated page (or it's simply the first page of a paginated page/post)

}
else
{
   // This is a paginated page.

}
?>

<?php
$paged = get_query_var( 'page' ) ? get_query_var( 'page' ) : false;
if ( $paged === false )
{
    // This is not a paginated page (or it's simply the first page of a paginated page/post)

}
else
{
   // This is a paginated page.

}
?>

Neither seem to detect whether or not there is another page or not–on the first page.

What we’ve been trying to get at, is a way to show or hide a div container depending on if there is paginated Pages for the post.

So; if isset($paged){
<div></div>
}

Is what I was hoping just might work.

We appreciate any help, thanks!