What are primitive roots modulo n? - Mathematics Stack Exchange
The important fact is that the only numbers $n$ that have primitive roots modulo $n$ are of the form $2^\varepsilon p^m$, where $\varepsilon$ is either $0$ or $1$, $p$ is an odd prime, and $m\ge0$
Show that $2$ is a primitive root modulo $13$.
I thought $\varphi (12)$ counts the number of coprimes to $12$.. Why does this now suddenly tell us the number of primitive roots modulo $13$? How have these powers been plucked out of thin air? I …
Finding a primitive root of a prime number
May 16, 2023 · 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
Understanding Primitive roots - Mathematics Stack Exchange
Jun 18, 2015 · Moreover the other primitive elements are obtained as powers of $2$ that are not the ones relevant to checking that $2$ is primitive, so you'd have to separately compute those powers …
calculus - Why is "antiderivative" also known as "primitive ...
Jan 6, 2019 · While antiderivative, primitive, and indefinite integral are synonymous in the United States, other languages seem not to have any equivalent terms for antiderivative. As others have pointed out …
elementary number theory - Find all the primitive roots of $13 ...
Jun 6, 2016 · Primes have not just one primitive root, but many. So you find the first primitive root by taking any number, calculating its powers until the result is 1, and if p = 13 you must have 12 …
euclidean algorithm - Proof of Euclid's formula for primitive ...
Jul 6, 2019 · I have been reading about Pythagorean triples from the wiki page link here. It says that a pythagorean triple consists of 3 positive integer's $ a, b, c $ such that $ a^2 + b^2 = c^2 $. Also if a...
finite fields - Understanding Primitive Polynomials in GF (2 ...
After you have one primitive polynomial, you often want to find other closely related ones. For example, when calculating generating polynomials of a BCH-code or an LFSR of a Gold sequence (or other …
complex analysis - Do holomorphic functions have primitive ...
Mar 16, 2022 · There is a very deep connection between the shape of $\Omega$ and the existence of primitives on $\Omega$. For now, let's assume that $\Omega$ is connected. Then it can be shown …
Is $x$ always a primitive element of $\text {GF} (2^m)$?
Apr 16, 2021 · Your last comment is the key. IIRC Matlab uses primitive polynomials by default (some coding theoretical apps need a primitive polynomial, and Matlab is a big seller in telcomm).