# How to calculate primitive root of a prime number

Mar 06, · Hint: since $h$ is non-zero mod $p$ it must be equal to $g^k$ for some positive integer $k$ (since $g$ is a primitive root). Now try to deduce something about $k$ knowing .

**Proof: Every Prime has a Primitive Root**

A primitive root mod n n n is an integer g g g such that every integer relatively prime to n n n is congruent to a power of g g g mod n n n. That is, the. We choose p to be such that p = 2 k + 1 where k is also a prime. It is relatively fast to find such p. Then any number in Z p ∗ will have an order which is one of 2, k, 2 k, 1. We pick a random .

Apr 23, · This is easy if you know the factorization of $p-1$; that is, $x$ is a primitive root if, for all prime factors $s$ of $p-1$, we have $x^{(p-1)/s} \not\equiv 1 \pmod p$ We can also .

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