I have not seen a problem like this before so I would be very grateful for some for some guidance. the problem is to find the gcd(100! + 99, 100! - 99). I know that both numbers are odd and that they can be rewritten as 99(100(98!) +1) and 99(100(98!) - 1) but I can't find my way from here.

the other problem is similar; find the gcd(2^2012 -1, 2^1776 -1)

Thanks for any help!!