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 …

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 …

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 …

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 …

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 $\phi (n)$ …

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 $p$.

Dec 30, 2020 · There are primitive roots mod n n if and only if n = 1, 2, 4,pk, 2pk n = 1, 2, 4, p k, 2 p k, where p p is an odd prime. The question is, for such general n n given as above (with n ≠ …

Sep 6, 2016 · Good day! I'm currently studying on the primitive roots mod n. Eventually, I fully understand the concept of calculating the primitive roots of a number by practice, but I …

Jan 28, 2017 · Artin-Wedderburn matrix decomposition holds for every semisimple ring. The first chapter of T.Y. Lam's book "A first course in noncommutative rings" should have everything …