Primitive root of a prime number n modulo n

Given a prime number n, the task is to find its primitive root under modulo n. The primitive root of a prime number n is an integer r between[1, n-1] such that the values of r^x(mod n) where x is in the range[0, n-2] are different. Return -1 if n is a non-prime number.

Examples:  

Input : 7
Output : Smallest primitive root = 3
Explanation: n = 7
3^0(mod 7) = 1
3^1(mod 7) = 3
3^2(mod 7) = 2
3^3(mod 7) = 6
3^4(mod 7) = 4
3^5(mod 7) = 5

Input : 761
Output : Smallest primitive root = 6 

A simple solution is to try all numbers from 2 to n-1. For every number r, compute values of r^x(mod n) where x is in the range[0, n-2]. If all these values are different, then return r, else continue for the next value of r. If all values of r are tried, return -1.

An efficient solution is based on the below facts. 
If the multiplicative order of a number r modulo n is equal to Euler Totient Function ?(n) ( note that the Euler Totient Function for a prime n is n-1), then it is a primitive root. 

1- Euler Totient Function phi = n-1 [Assuming n is prime]
1- Find all prime factors of phi.
2- Calculate all powers to be calculated further 
 using (phi/prime-factors) one by one.
3- Check for all numbered for all powers from i=2 
 to n-1 i.e. (i^ powers) modulo n.
4- If it is 1 then 'i' is not a primitive root of n.
5- If it is never 1 then return i;.

Although there can be multiple primitive roots for a prime number, we are only concerned with the smallest one. If you want to find all the roots, then continue the process till p-1 instead of breaking up by finding the first primitive root. 

Output:  

Smallest primitive root of 761 is 6

Time Complexity : O(n^2 * logn)
Space Complexity : O(sqrt(n))