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. …

Jan 3, 2015 · 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

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. …

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 …

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 unity by …

Nov 12, 2024 · So if there are any primitive elements and we're working in characteristic zero, then the n n th power of each primitive will satisfy your property. Note that the n n th power xn x n of a primitive …

Oct 31, 2015 · The primitive of a continuous function on a compact interval is continuous via the Fundamental Theorem of Calculus. Let I ⊂R I ⊂ R be open and let u′: I¯¯¯ ↦R u: I ↦ R be continuous.

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.

In general, the primitive n n th roots of unity in the n n th cyclotomic field form a normal basis over Q Q if and only if n n is squarefree. A little bit of research didn't turn up any results, except apparently the …

Nov 30, 2014 · I'm trying to go in a kind of unconventional route and prove the existence of a primitive root \mathchoice (mod p) \mathchoice (mod p) (where p p is a prime) using group theory.