Hi, I have 3 problems concerning primitive roots that I have been unable to work through. Any advice on how to solve these would be greatly appreciated!

1. Show if g, h are primitive roots of p and p is odd, the least residue of gh is not a primitive root of p.

2. Show 131071 = (2^17)-1 is prime.

3. Show that k exists such that g^(k+1)=(g^k)+1 (mod p), where g is a primitive root of p and p is a prime.

Thanks in advance!