How to remove query string page from the first page of laravel pagination?

I'm using laravel-5.4 pagination like the following:

public function index()
    {
        $jobs = Job::paginate(5);
        return view('job.index', compact('jobs'));
    }

In the view:

{{ $jobs->links() }}

There is a problem of generating two typical pages: /job and /job?page=1 the two page has the same contents.

I want to do anything that removes the query string page from the first page of the pagination.

I have tried the following:

if ($jobs->onFirstPage()){
  $jobs->setPageName('');
} 

But this corrupt the pagination, i.e the links of pages does not load correctly and the query string value remains for all pages.

The effective solution for this issue that I have found is to edit the pagination template.

First publish the pagination template from the vendors using the following command from the root of the project:

php artisan vendor:publish --tag=laravel-pagination

Now a file at resources/views/vendor/pagination/default.blade.php should be found and it could be edited like the following using str_replace() for the urls of each page and back navigation button:

<li><a href="{{str_replace('?page=1','',$paginator->previousPageUrl())}}" title="{{__('Previous')}}" rel="prev">{{$foxPrev}}</a></li>

and

 <li><a href="{{str_replace('?page=1','',$url)}}">{{ $page }}</a></li>

Update:

A bug was found with ?page=10 so instead of using str_replace we should using preg_replace like the following:

<li><a href="{{preg_replace('/\?page=[1]$/','',$url)}}">{{ $page }}</a></li>

Update 2:

In case of using any customized name for the page number parameter other than page, we could use the paginator getter for the $pageName property like the following in the pagination template:

<li><a href="{{preg_replace('/\?'.$paginator->getPageName().'=[1]$/','',$url)}}">{{ $page }}</a></li>

To know more about how to use more than one pagination on the same page or how to customize the page number parameter $pageName from view, checkout this answer