"page" GET attribute turns into a URL rewrite

Hi guys, I have a little issue with my current WP project.

I know the title may not be really clear but the issue itself looks weird, let me explain :
(I’m under NDA so I won’t be too specific about content.)

I’m using WP_Query on several pages of my site to show custom post types.
I’m currently implementing a custom paging system.

One of my pages shows “generic results”, and I’m using GET parameters to fetch items.

I added a “page” parameter to show paged content. This parameter is supposed to be intercepted by the script to alter the WP Query.

For instance, if I want to show the page 3, i simply append “page=3” to my permalink.

So I got this :

https://myprojectpath/show/?page=3

Problem is, instead of letting the URL as is and using the page GET variable, WordPress rewrites the URL to this :

https://myprojectpath/show/3/

Which BTW makes my script fail as there is no “page” information.

FYI, this method works fine on my site home page.

Thank you.