Jan 6, 2019 · The so-called primitive function f f, which was the starting point and so came first, the root meaning of primitive (Lat. primus, first), is what we might call an antiderivative or …

Mar 23, 2019 · There are indeed ϕ(ϕ(31)) = 8 ϕ (ϕ (31)) = 8 primitive roots modulo 31 31 and you can find them as described here: Finding a primitive root of a prime number For example, 3k ≡ …

Jan 21, 2012 · Show that the primitive n-th roots of unity have the form e2kiπ/n e 2 k i π / n for k, n k, n coprime for 0 ≤ k ≤ n 0 ≤ k ≤ n. Since all primitive n-th roots of unity are n-th roots of …

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 $\phi (n)$ …

Jun 17, 2015 · I am trying to solve the following exercise in Koblitz's " p p -adic Numbers, p p -adic analysis, and Zeta-Functions". Let p p be a prime. Let a a be a primitive pn p n -th root of unity …

Apr 5, 2015 · Maximal Subgroups and Point Stabilizers of Primitive Group Actions Ask Question Asked 10 years, 9 months ago Modified 10 years, 9 months ago

Sep 29, 2023 · There is only one primitive quadratic Dirichlet character modulo N N, namely the one induced by (Δ(⋅) (Δ ( ⋅ ), where Δ Δ is the discrimininant with absolute value N N.

Apr 29, 2019 · Let a a be a primitive root modulo odd prime. Show that in an arithmetic progression a + kp a + k p, where k = 0, 1, …, p − 1 k = 0, 1,, p 1 there is exactly one number …

The problem/solution of counting the number of (primitive) necklaces (Lyndon words) is very well known. But what about results giving sufficient conditions for a given necklace be primitive? …

Mar 5, 2018 · Example of searching another primitive root. $3$ is a primitive root modulo $7$ and $\phi (7)=6$. Thus $3^5=5$ modulo $7$ is the only other p.r. because $2,3,4,6$ are not …