Jan 3, 2015 · How would you find a primitive root of a prime number such as 761? How do you pick the primitive roots to test? Randomly? Thanks

I'm trying to understand what primitive roots are for a given mod n mod n. Wolfram's definition is as follows: A primitive root of a prime p p is an integer g g such that g (mod p) g (mod p) has …

Jan 6, 2019 · The so-called primitive function f f, which was the starting point and so came first, the root meaning of primitive (Lat. primus, first), is what we might call an antiderivative or integral of p p. …

Jul 14, 2014 · It can be proven that a primitive root modulo $n$ exists if and only if $$n \in \ { 1,2 , 4, p^k, 2 p^k \}$$ with $p$ odd prime. For each $n$ of this form there are exactly $\phi (n)$ primitive roots.

9 What is a primitive polynomial? I was looking into some random number generation algorithms and 'primitive polynomial' came up a sufficient number of times that I decided to look into it in more detail. …

Mar 23, 2019 · There are indeed ϕ(ϕ(31)) = 8 ϕ (ϕ (31)) = 8 primitive roots modulo 31 31 and you can find them as described here: Finding a primitive root of a prime number For example, 3k ≡ 1 mod 31 …

Jul 23, 2018 · 6 So I encountered this proof on a Number Theory book, I will link the pdf at the end of the post (proof at page 96), it says: " Every prime has a primitive root, proof: Let p be a prime and let m …

Mar 5, 2018 · Example of searching another primitive root. $3$ is a primitive root modulo $7$ and $\phi (7)=6$. Thus $3^5=5$ modulo $7$ is the only other p.r. because $2,3,4,6$ are not coprime with $6$ …

Jan 21, 2012 · Show that the primitive n-th roots of unity have the form e2kiπ/n e 2 k i π / n for k, n k, n coprime for 0 ≤ k ≤ n 0 ≤ k ≤ n. Since all primitive n-th roots of unity are n-th roots of unity by …

Jul 12, 2012 · Notice that, since $a$ is a primitive root modulo $p$, $a^ { (p-1)/2}$ must be congruent to a square root of 1, but at the same time different from 1, modulo $p$.