This video describes what a primitive roots is. Also, how to test if a number (alpha) is primitive for a low/small modulus. Also note that there is a more efficient way of testing for a primitive root (if p-1 is easily factorable), which is discussed in part 2: https://www.youtube.com/wat
From playlist Number Theory
The second method for testing whether alpha is a primitive root mod p. Description of primitive roots is in the Primitive Roots pt. 1 video. Questions? Feel free to post them in the comments and I'll do my best to answer!
From playlist Number Theory
Number Theory | Primitive roots modulo p -- Technical Lemma 2
We present another technical lemma regarding primitive roots modulo p. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Primitive Roots Modulo n
Number Theory | Existence of an mth root modulo n
We present a Theorem that discusses the existence of an mth root modulo n, given that there is a primitive root modulo n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Primitive Roots Modulo n
Theory of numbers: Congruences: Primitive roots
This lecture is part of an online undergraduate course on the theory of numbers. We define primitive roots, and show that all primes have primitive roots. Correction: At 16:00 two of the square roots of 1 should be (2^k)/2 +1, (2^k)/2-1, not 2^k/2, -2^k/2. For the other lectures in th
From playlist Theory of numbers
Vortrag "Wo steht die mathematische Forschung?"
Im Jahr 2000 veröffentlichte das Clay Mathematics Institute eine Liste von sieben großen mathematischen Problemen. Diese Millennium-Probleme wurden damals als die zentralen Fragen der Mathematik angesehen. Sie sind – mit nur einer Ausnahme, der Poincaré-Vermutung – bis heute ungelöst. Zu d
From playlist Riemannsche Vermutung
Kiran Kedlaya, The Sato-Tate conjecture and its generalizations
VaNTAGe seminar on March 24, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Peter Stevenhagen: Character sums for primitive root densities
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Jean-Morlet Chair - Shparlinski/Kohel
José Felipe Voloch: Generators of elliptic curves over finite fields
Abstract: We will discuss some problems and results connected with finding generators for the group of rational points of elliptic curves over finite fields and connect this with the analogue for elliptic curves over function fields of Artin's conjecture for primitive roots. Recording du
From playlist Number Theory
Primitive Roots - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Applications of primitive roots -- Number Theory 19
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Number Theory v2
Number Theory | There is a primitive root modulo every power of an odd prime!!
We prove that for an odd prime p, there is a primitive root modulo p^n for all natural numbers n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Primitive Roots Modulo n
p-adic Artin L-function over a CM-field by Tadashi Ochiai
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Primitive Roots Solution - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Perfectoid spaces (Lecture 2) by Kiran Kedlaya
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Jörg Thuswaldner: S-adic sequences: a bridge between dynamics, arithmetic, and geometry
Abstract: Based on work done by Morse and Hedlund (1940) it was observed by Arnoux and Rauzy (1991) that the classical continued fraction algorithm provides a surprising link between arithmetic and diophantine properties of an irrational number αα, the rotation by αα on the torus 𝕋=ℝ/ℤT=R/
From playlist Dynamical Systems and Ordinary Differential Equations
Number Theory | There are no primitive roots modulo 2^n!!
We prove that for n greater than 2, there are no primitive roots modulo 2^n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
Multiplicities in Selmer Groups and Root Numbers for Artin Twists by Tathagata Mandal
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Number Theory | Products of primitive roots modulo p
We prove a statement regarding the product of primitive roots modulo p. This is nice example for working with an abstract statement involving primitive roots. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Primitive Roots Modulo n
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties