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 find primitive root modulo of 23? [duplicate] These types of questions are repeated here zillionth time, but I am yet to find an useful process (hit and trial or any other process) to find primitive root modulo
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
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 $p$
Basis of primitive nth Roots in a Cyclotomic Extension? Another method to show the "only if " direction is to use the fact that the trace of $\zeta_n$ is equal to zero if n is not square free, while by definition, the trace of $\zeta_n$ in this case is exactly the same as the sum of all the primitive n-th roots of unity, so we have a linearly dependent relation over $\mathbb {Q}$ for all the primitive n-th roots, so they could not form a basis, see
Primitive roots modulo n - Mathematics Stack Exchange 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
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
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