please i need help in foloowing propems

1) if r is primitive root of , then r is a primitive root of ,

[hint: use induction of i ]

2) le t be a prime , r be any primitive root of p , let a be any positive integer with gcd(a,p)=1 , then ; prove that iff

3) let p be prime , r any primitive root of p , let a be any (+ve) integer such that gcd(a,p)=1 then prove that the order of a modoulo p is

4) show that if , ,then