Additive number theory | Squares in number theory | Theorems in number theory | Articles containing proofs
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four. where the four numbers are integers. For illustration, 3, 31, and 310 in several ways, can be represented as the sum of four squares as follows: This theorem was proven by Joseph Louis Lagrange in 1770. It is a special case of the Fermat polygonal number theorem. (Wikipedia).
2023 Number Challenge: Find sum of four squares that is equal to 2023
#mathonshorts #shorts check out wiki page: https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares.
From playlist Math Problems with Number 2023
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Group theory 4: Lagrange's theorem
This is lecture 4 of an online course on mathematical group theory. It introduces Lagrange's theorem that the order of a subgroup divides the order of a group, and uses it to show that all groups of prime order are cyclic, and to prove Fermat's theorem and Euler's theorem.
From playlist Group theory
We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at
From playlist Abstract algebra
Abstract Algebra | Lagrange's Theorem
We prove some general results, culminating in a proof of Lagrange's Theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Chapter 3: Lagrange's theorem, Subgroups and Cosets | Essence of Group Theory
Lagrange's theorem is another very important theorem in group theory, and is very intuitive once you see it the right way, like what is presented here. This video also discusses the idea of subgroups and cosets, which are crucial in the development of the Lagrange's theorem. Other than c
From playlist Essence of Group Theory
Lagrange's Theorem and Index of Subgroups | Abstract Algebra
We introduce Lagrange's theorem, showing why it is true and follows from previously proven results about cosets. We also investigate groups of prime order, seeing how Lagrange's theorem informs us about every group of prime order - in particular it tells us that any group of prime order p
From playlist Abstract Algebra
Number Theory | Lagrange's Theorem of Polynomials
We prove Lagrange's Theorem of Polynomials which is related to the number of solutions to polynomial congruences modulo a prime.
From playlist Number Theory
Abstract Algebra - 7.2 LaGrange’s Theorem and Consequences
In this video we explore Lagrange's Theorem, which tells us some important information about both the order of a subgroup of a group, as well as the number of distinct cosets we can expect given a certain subgroup H. Video Chapters: Intro 0:00 LaGrange's' Theorem 0:07 Consequences of LaGr
From playlist Abstract Algebra - Entire Course
Maximize a Function of Two Variable Under a Constraint Using Lagrange Multipliers
This video explains how to use Lagrange Multipliers to maximize a function under a given constraint. The results are shown in 3D.
From playlist Lagrange Multipliers
Lagrange's Theorem -- Abstract Algebra 10
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From playlist Abstract Algebra
Cosets and Lagrange’s Theorem - The Size of Subgroups (Abstract Algebra)
Lagrange’s Theorem places a strong restriction on the size of subgroups. By using a device called “cosets,” we will prove Lagrange’s Theorem and give some examples of its power. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We re
From playlist Abstract Algebra
Calculus BC - Unit 5 Lesson 2: Lagrange Error Bound
Calculus BC - Taylor's Remainder Theorem and the Lagrange Error Bound
From playlist AP Calculus BC
Richard Pinch: Fermat's Last Theorem [1994]
Richard Pinch: Fermat's Last Theorem Based on the 1994 London Mathematical Society Popular Lectures, this special 'television lecture' entitled "Fermat's last theorem" is presented by Dr Richard Pinch. The London Mathematical Society is one of the oldest mathematical societies, founded i
From playlist Mathematics
Subderivatives and Lagrange's Approach to Taylor Expansions | Algebraic Calculus Two | Wild Egg
The great Italian /French mathematician J. L. Lagrange had a vision of analysis following on from the algebraic approach of Euler (and even of Newton before them both). However Lagrange's insights have unfortunately been largely lost in the modern treatment of the subject. It is time to re
From playlist Algebraic Calculus Two
Deriving Noether's Theorem: How Symmetry Leads to Conservation. GAOMON PD1560 for Online Teaching!
Today I derive the conserved current from a continuous global symmetry of the lagrangian. I do this both in the context of field theory with tensor notation, and in regular classical mechanics with generalized coordinates and time derivatives. I provide a way of translating from the tensor
From playlist Math/Derivation Videos
Dynamical systems, fractals and diophantine approximations – Carlos Gustavo Moreira – ICM2018
Plenary Lecture 6 Dynamical systems, fractal geometry and diophantine approximations Carlos Gustavo Moreira Abstract: We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related
From playlist Plenary Lectures
Non-Hermiticity: A New Paradigm for Model Building in Particle Physics by Peter Millington
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Lagrange Multipliers: Minimize f=x^2+y^2 under Constraint x+4y=20
This video provides and example of how to use the method of Lagrange Multipliers.
From playlist Lagrange Multipliers