calculus - Why is "antiderivative" also known as "primitive ...
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 integral of p p. …
Primitive roots in arithmetic progression - Mathematics Stack Exchange
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 that is NOT a primitive …
When are Idempotents elements of a semisimple algebra primitive
Jun 26, 2024 · 1 Based on the comments, a primitive central idempotent is a central idempotent that cannot be written as a sum of two central orthogonal idempotents. If we define that a primitive …
algebraic number theory - Proving Dirichlet character is primitive ...
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.
Are all natural numbers (except 1 and 2) part of at least one primitive ...
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 …
primitive idempotents in semisimple rings - Mathematics Stack Exchange
Jan 28, 2017 · Artin-Wedderburn matrix decomposition holds for every semisimple ring. The first chapter of T.Y. Lam's book "A first course in noncommutative rings" should have everything you need.
logic - To what extent can Primitive Recursion perform wellfounded ...
Jul 31, 2024 · In fact, primitive recursive functions can perform a huge variety of set-theoretic tasks, which makes primitive wellfounded recursion straightforward... Or at least, it's straightforward to …
Primitive Roots modulo p - Mathematics Stack Exchange
I'm asked the following question: Prove that b b is a primitive root modulo p p the smallest positive exponent e e such that be ≡ 1 (mod p) b e ≡ 1 (mod p) is p − 1 p 1. I know that this could probably be …
Find the Primitive Roots - Mathematics Stack Exchange
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 ≡ 1 mod 31 …
Primitive roots modulo n - Mathematics Stack Exchange
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.