Introduction to Solving Linear Diophantine Equations Using Congruence
This video defines a linear Diophantine equation and explains how to solve a linear Diophantine equation using congruence. mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
From playlist L. Number Theory
Diophantine Equations: Polynomials With 1 Unknown ← number theory ← axioms
Learn how to solve a Diophantine Equation that's a polynomial with one variable. We'll cover the algorithm you can use to find any & all integer solutions to these types of equations. written, presented, & produced by Michael Harrison #math #maths #mathematics you can support axioms on
From playlist Number Theory
Solve Diophantine Equation by Factoring
#shorts #mathonshorts
From playlist Elementary Number Theory
Theory of numbers: Linear Diophantine equations
This lecture is part of an online undergraduate course on the theory of numbers. We show how to use Euclid's algorithm to solve linear Diophantine equations. As a variation, we discuss the problem of solving equations in non-negative integers. We also show how to solve systems of linear D
From playlist Theory of numbers
Number Theory | Linear Diophantine Equations
We explore the solvability of the linear Diophantine equation ax+by=c
From playlist Divisibility and the Euclidean Algorithm
Linear Diophantine Equations with 3 Variables - 3 Different Methods
We want to solve the linear Diophantine equation with 3 variables: 35x+55y+77z=1 for integer solutions in Three methods are discussed: 1. Split the equation into two linear equation each of which has two variables. 2. Parameterize with canonical form 3. Particular solution and general
From playlist Diophantine Equations - Elementary Number Theory
The Most Difficult Math Problem You've Never Heard Of - Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a millennium prize problem, one of the famed seven placed by the Clay Mathematical Institute in the year 2000. As the only number-theoretic problem in the list apart from the Riemann Hypothesis, the BSD Conjecture has been haunting mathematicians
From playlist Math
Barry Mazur - Logic, Elliptic curves, and Diophantine stability
This is the first lecture of the 2014 Minerva Lecture series at the Princeton University Mathematics Department October 14, 2014 An introduction to aspects of mathematical logic and the arithmetic of elliptic curves that make these branches of mathematics inspiring to each other. Specif
From playlist Minerva Lectures - Barry Mazur
Henri Darmon: Andrew Wiles' marvelous proof
Abstract: Pierre de Fermat famously claimed to have discovered “a truly marvelous proof” of his last theorem, which the margin in his copy of Diophantus' Arithmetica was too narrow to contain. Fermat's proof (if it ever existed!) is probably lost to posterity forever, while Andrew Wiles' p
From playlist Abel Lectures
Yuri Matiyasevich - On Hilbert's 10th Problem [2000]
On Hilbert's 10th Problem - Part 1 of 4 Speaker: Yuri Matiyasevich Date: Wed, Mar 1, 2000 Location: PIMS, University of Calgary Abstract: A Diophantine equation is an equation of the form $ D(x_1,...,x_m) $ = 0, where D is a polynomial with integer coefficients. These equations were n
From playlist Number Theory
Introduction to Diophantine equations
This is an introductory talk on Diophantine equations given to the mathematics undergraduate student association of Berkeley (https://musa.berkeley.edu/) We look at some examples of Diophantine equations, such at the Pythagoras equation, Fermat's equation, and a cubic surface. The main th
From playlist Math talks
Diophantine approximation and Diophantine definitions - Héctor Pastén Vásquez
Short Talks by Postdoctoral Members Héctor Pastén Vásquez - September 29, 2015 http://www.math.ias.edu/calendar/event/88264/1443549600/1443550500 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
N J Wildberger Research Snapshot: The power method for Diophantine equations
A/Prof N J Wildberger gives a quick introduction to his research work on the power method for solving general Diophantine equations. This is a Research Snapshot from the School of Mathematics and Statistics, Faculty of Science, UNSW.
From playlist Research Snapshots
Diophantine Equation: ax+by=gcd(a,b) ← Number Theory
Once you know how to solve diophantine equations with a single variable, the next step in complexity is to consider equations with two variables. The simplest such equations are linear and take the form ax+by=c. Before we solve this equation generally, we need a preliminary result. We s
From playlist Number Theory
The extended Euclidean algorithm in one simple idea
An intuitive explanation of the extended Euclidean algorithm as a simple modification of the Euclidean algorithm. This video is part of playlist on GCDs and the Euclidean algorithm: https://www.youtube.com/playlist?list=PLrm9Y---qlNxXccpwYQfllCrHRJWwMky-
From playlist GCDs and Euclidean algorithm
Theory of numbers:Introduction
This lecture is part of an online undergraduate course on the theory of numbers. This is the introductory lecture, which gives an informal survey of some of the topics to be covered in the course, such as Diophantine equations, quadratic reciprocity, and binary quadratic forms.
From playlist Theory of numbers
Alexander Gorodnik - Diophantine approximation and flows on homogeneous spaces (Part 3)
The fundamental problem in the theory of Diophantine approximation is to understand how well points in the Euclidean space can be approximated by rational vectors with given bounds on denominators. It turns out that Diophantine properties of points can be encoded using flows on homogeneous
From playlist École d’été 2013 - Théorie des nombres et dynamique