Unable to Confirm Facebook account identity on another computer

Hello,
I've been trying to confirm my identity, because my account was "mysteriously" accessed out of the blue. And it gives me the option, to confirm with recent comments, or to confirm with previous devices. I tried the previous comments challenge 3 times, and I know I got those comments right, but facebook still told me they couldn't recognize me. And then I tried to attempt the other option, which was to access through another device, but when I go and try to log on, on those other devices, the same confirmation pop-up shows. I need assistance, its really bugging me.