In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one. An exponential Diophantine equation is one in which unknowns can appear in exponents. Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves, algebraic surfaces, or, more generally, algebraic sets, their study is a part of algebraic geometry that is called Diophantine geometry. The word Diophantine refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra. The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis. While individual equations present a kind of puzzle and have been considered throughout history, the formulation of general theories of Diophantine equations (beyond the case of linear and quadratic equations) was an achievement of the twentieth century. (Wikipedia).
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
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
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
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
Train your Number Theory Expertise by trying out Brilliant! =D https://brilliant.org/FlammableMaths Support the channel by checking out Deez Nutz over on https://stemerch.eu/ ! :3 Wuck. https://play.google.com/store/apps/details?id=org.flammablemaths.Wuck Check out my newest video over on
From playlist Number Theory
Stars-and-Bars to Find the Number of Solutions of a Diophantine Equation!
In this video, we will be applying a well-known Combinatorics concept, Stars and Bars, to find the number of integer solutions to a Diophantine Equation. We will cover 2 problems: w+x+y+z = 10 Problem 1: how many solutions for w, x, y, z being non-negative integers? Problem 2: how many
From playlist Elementary Number Theory
Reducibility for the Quasi-Periodic Liner Schrodinger and Wave Equations - Lars Hakan Eliasson
Lars Hakan Eliasson University of Paris VI; Institute for Advanced Study February 21, 2012 We shall discuss reducibility of these equations on the torus with a small potential that depends quasi-periodically on time. Reducibility amounts to "reduce” the equation to a time-independent linea
From playlist Mathematics
A Short Course in Algebra and Number Theory - Elementary Number Theory
To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the fourth lectu
From playlist A Short Course in Algebra and Number Theory
Hakan Eliasson: Quasi-periodic wave equation - almost reducibility-
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 Dynamical Systems and Ordinary Differential Equations
Robert Tichy: Metric Discrepancy Theory
CIRM HYBRID EVENT Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the February 04, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathem
From playlist Analysis and its Applications
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