Polynomials over Z/pZ

preview_player
Показать описание
This is a short lecture about polynomials over Z/pZ (the integers mod p). We look at a few propositions regarding roots of polynomials over a field, and do some examples illustrating how these propositions work over Z/pZ, but may fail over Z/nZ when n is composite.
  1. Andrew McCrady
  2. polynomials
  3. primes
  4. Z/pZ
  5. zero product property
  6. roots
Рекомендации по теме
Polynomials over Z/pZ 0:19:54

Polynomials over Z/pZ

Roots of polynomials 0:30:47

Roots of polynomials over Zp

Nathan Kaplan, 'Codes 0:53:39

Nathan Kaplan, 'Codes from polynomials over finite fields'

Week 5-Lecture 22 0:30:47

Week 5-Lecture 22 : Roots of polynomials over ℤp

What are...irreducible polynomials? 0:18:16

What are...irreducible polynomials?

Abstract Algebra, Lec 0:26:19

Abstract Algebra, Lec 29B: Polynomial Irreducibility/Reducibility Theorems and Examples

Lesson Cx.7A - 0:08:38

Lesson Cx.7A - Factoring Polynomials Over the Complex Field

Abstract Alg, 28B: 0:25:50

Abstract Alg, 28B: F[x] is a Principal Ideal Domain, Irreducibility over Integral Domains & Fiel...

If a Polynomial 0:04:47

If a Polynomial has a Zero of Order m, it's Derivative has a Zero of Order m-1 Proof

Factorising Polynomials over 0:11:01

Factorising Polynomials over C worked examples

Galois theory: Cyclotomic 0:22:18

Galois theory: Cyclotomic polynomials

Will Sawin: The 0:49:58

Will Sawin: The distribution of prime polynomials over finite fields (NTWS 047)

Solving Polynomials | 0:25:45

Solving Polynomials | HSC Extension 2 Mathematics

Lec 10 Polynomials 0:59:27

Lec 10 Polynomials Over Fields

One of the 0:36:37

One of the most important algebras -- The Witt Algebra

Splitting Fields of 0:22:32

Splitting Fields of Polynomials over Finite Fields (Algebra 3: Lecture 23 Video 1)

Complex Polynomials (Part 0:21:04

Complex Polynomials (Part 7 of 7): Higher Degree Equations 4

mod09lec45 - Algebras 0:34:12

mod09lec45 - Algebras over a field

Factorizing complex polynomials 0:10:19

Factorizing complex polynomials

Real Linear and 0:14:22

Real Linear and Quadratic Factors of a Polynomial (Ch3 Pr74)

The discrete Fourier 0:30:44

The discrete Fourier uncertainty principle: III. Basics of cyclotomic polynomials

4 Polynomials 0:45:02

4 Polynomials

Showing x^4+1 is 0:14:51

Showing x^4+1 is reducible over Z_p

8. Complex Polynomials 0:09:19

8. Complex Polynomials Intro