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 $m\ge0$
Primitive and modular ideals of $C^ {\ast}$-algebras So $\ker\pi$ is primitive but not modular To find a modular ideal that is not primitive, we need to start with a unital C $^*$ -algebra (so the quotient will be unital) and consider a non-irreducible representation
The primitive $n^ {th}$ roots of unity form basis over $\mathbb {Q . . . We fix the primitive roots of unity of order $7,11,13$, and denote them by $$ \tag {*} \zeta_7,\zeta_ {11},\zeta_ {13}\ $$ Now we want to take each primitive root of prime order from above to some power, then multiply them When the number of primes is small, or at least fixed, the notations are simpler
Finding a primitive root of a prime number 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
How to identify a group as a primitive group? PrimitiveIdentification requires the group to be a primitive group of permutations, not just a group that can be primitive in some action You will need to convert to a permutation group, most likely by acting on the set of $23^2$ vectors
number theory - Show that if a quadratic form is primitive then so are . . . A Quadratic form is primitive if the greatest common divisor of the coefficients of it's terms is 1 I saw in number theory book that "it is easily seen that any form equivalent to a primitive form is also primitive" but I cannot seem to show this to be true myself
What are prime and primitive polynomials? - Mathematics Stack Exchange I will really appreciate if someone could give example of these and explain what makes them primitive and prime e g about polynomials used in Cyclic Redundancy Check that are implemented using hardware feedback registers it says "The best ones are not necessarily prime (irreducible) nor primitive"
Are all natural numbers (except 1 and 2) part of at least one primitive . . . Hence, all odd numbers are included in at least one primitive triplet Except 1, because I'm not allowing 0 to be a term in a triplet I can't think of any primitive triplets that have an even number as the hypotenuse, but I haven't been able to prove that none exist
What is a primitive polynomial? - Mathematics Stack Exchange 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 I'm unsure of what a primitive polynomial is, and why it is useful for these random number generators
Equivalent definition of primitive Dirichlet character A character is non-primitive iff it is of the form $1_ {\gcd (n,k)=1} \psi (n)$ with $\psi$ a character $\bmod m$ coprime with $k$ A character $\bmod p^2$ can be primitive with conductor $p$