Lost App Icon

I was recently playing around with my iphone apps and moving the icons around and soon realized I lost the Facebook app. I looked all over, every page, and it just vanished! So I thought I just deleted it on accident.

So, I went to iTunes hit sync, and it still wasn't there. So, I removed the app completely from iTunes and hit sync, and then downloaded the app from the app store, and hit sync, and still not Facebook. So, I tried unchecking the box next to the apps to install and then checking it after another sync, and still no facebook app.

So, again I deleted it completely from iTunes and hit sync and it said it removed the app. So then I went to App store on my iphone and was going to download it, but it wouldn't let me saying it was already on my iPhone.

I did hard resets, turned it off for several minutes, factory default resets both with facebook app in iTunes and not in iTunes backed up. I have tried just about everything.

Can anyone help me please. I have thought about doing a factory default reset again, but not reload my backup files and just start from scratch, but don't want to. Just hoping someone can help me with this. Where is my app?