We know that means since is odd we can write . Now it cannot be because . Thus, the only possibility is that .

We can write where . For be a primitive root it is necessary and sufficient that . Now , now for to be a primitive root it is necessary and sufficient that . But that is impossible because is an even number and among one is even by pigeonholing. Thus it impossible for to be a primitive root canal.b) if r' is any other primitive root of p , then rr' is not primitive root of p.

Now, because , thus, that means we can write for . We have that by hypothesis. That means because the order of is and . Thus , so and it means it is a primitive root.c) if the integer r' is such that rr'=1(mod p) then r' is primitive root of p.