Facebook - Like the Page or App, or Like the Site URL?

I've been working on a passion-project for a while called Pi Day Challenge - it's a site designed to inspire people about math and celebrate 3/14.

One thing that I thought about tonight was whether or not I should direct users to like the app/fan page (http://facebook.com/pidaychallenge ) or the site itself (http://pidaychallenge.com ).

What's the best practice in a case like this - app or site?

Upsides I see to liking the app url:

• I already have 700+ likes on the app itself
• We interact with fans on this page - it's like a pseudo Facebook page with a feed, etc.
• If a user likes the app url, they become a fan of that page, and news shows up in their feed (I think)

• When friends see their friends like it, the URL they click brings them directly to the site. When they like the app url, it instead brings them to http://facebook.com/pidaychallenge and then they have to click "Go to App" to actually use it.
• Could potentially give link love to the actual site - but I'm not sure

If you're looking for link love, I think a +1 button on your site is the way to go. Facebook likes to your URL provide No Link Juice. If you're looking to build awareness I would go to the facebook page, if you are trying to move apps, maybe the URL is a better choice.

I'm with choosing the URL method.

That way it can help you gain publicity easier. If a person can view your site and (likes it), they will look for the mobile app as well.