iPhone asking for Apple ID for a former roommate
I suppose you restored your iPhone 6 from a backup of your older phone. If I understand the issue well enough, the phone keeps asking you for your friend password because you have an app that is his. If this app is on your computer in iTunes, there is a solution.

In the iTunes' list view of your Apps, right-click on an app, "Get info" (or just press cmd ⌘+I), and, depending on your OS version, either go to the Summary or the File tab. The Apple ID of the buyer, as well as his name, will appear, and you just have to go through your files (pressing cmd ⌘+P and cmd ⌘+N) until you find the culprit. 

Unfortunately, iTunes cannot sort apps by buyer. However, you could sort Apps by "Date Added" in the list view to make the whole process much easier.