please i need help in foloowing propems

1) if r is primitive root of $\displaystyle p^k $, then r is a primitive root of $\displaystyle p^i$ , $\displaystyle 1<i<k$

[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 $\displaystyle r^n\equiv a(modp)$ iff $\displaystyle a\equiv ind a(mod p^-1)$

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 $\displaystyle \phi(p)/gcd(\phi(p),inda)$

4) show that if $\displaystyle a^k\equiv1(modp) $,$\displaystyle a^h\equiv1(modp)$ ,then $\displaystyle a^hp\equiv 1(modp^2)$