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 $m\ge0$

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

Apr 10, 2024 · 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 …

Jul 31, 2023 · 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 …

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 $\phi (n)$ primitive roots.

Mar 2, 2022 · Let $ G $ be a subgroup of $ SU_n $ which is maximal among the proper closed subgroups of $ SU_n $. Must $ G $ be primitive? Recall that we say a subgroup $ G $ of $ …

Apr 21, 2020 · "If the $n$ having primitive root,$g$ , there are some quadratic residue that can be expressed as a $g^ {2k}$" (Because of the counterexample you suggested $p^2$ is a quadratic …

Nov 5, 2025 · 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 …

May 31, 2016 · 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 …

Checking per Gerry's suggestion, a quick spreadsheet for the 40 primitive roots mod 101 shows that twenty-six (26) of them are square-free and fourteen (14) of them are not. We are helped in this by …