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
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
Primitive positive integer solutions of $a^4 + b^4 + c^4 = d^4 + kabcd$ Within the conventional range of $a \le b \le c \le 200$ and $d \le 1000000$, no primitive positive integer solution has been found for any of these 11 values of $k$, and constructing one using elliptic curve methods is extremely difficult
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
What is a free group element that is not primitive? A primitive element of a free group is an element of some basis of the free group I have seen some recent papers on algorithmic problems concerning primitive elements of free groups, for example,
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