Not necessarily an iOS 10 issue, but you guys might be able to help...
Just got an iPhone 7 (upgrading from a 6), and all is well apart from iTunes asking me every two minutes to sign in to two different accounts that aren't mine, presumedly to authorize some purchases in my library.
One of these people I don't even speak to anymore. Any ideas?
If you can;t sign in, the best thing actually is to identify what those purchases are and remove them from your computer.
OH wait, you mean your phone. Same deal though. Find out what those are (presumable apps), and get rid of them.