Complete Residue Systems Problem

Hello everyone, I have a question on complete residue systems that I do not understand.

1. Are there any twin primes (like 11 and 13, or 3 and 5) of the form (2^n)-1, (2^n) +1, for n > 2?

If there are, do you have an example? If not, could you explain why there aren't any?

2. Assume that m and n are integers where GCD[m,n]=1. Assume m and n are > 1. The set S={0*n,1*n,2*n,...,(m-1)*n} is a complete residue system modulo m. How can I prove this ?

Any help is appreciated!