In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integersolutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. An exponential Diophantine equation is one in which exponents on terms can be unknowns.
Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, and ask about the lattice points on it.
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.
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 show that you can solve the equation ax+by=GCD(a,b) by performing the Euclidean algorithm, and then reverse-substituting to arrive at a single solution.
Teacher: Michael Harrison
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: https://www.facebook.com/SocraticaStudios/
Instagram: https://www.instagram.com/SocraticaStudios/
Twitter: https://twitter.com...
published: 23 Jan 2012
A Nice Diophantine Equation in Number Theory | You Should Learn This Theorem | Math Olympiad
In this video, I am introducing a nice diophantine equation in number theory and also a wonderful theorem you can use to solve a linear diophantine equation with two unknown variables. With this theorem, most of the linear diophantine equations with two unknown variables will be nicely solved. Diophantine equation is an interesting topic in number theory. Come check this video out and watch it until the end. This would also be a good practice for math olympiad. More with diophantine equation problems will come! Stay tuned!
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ https://www.instagram.com/drpk...
published: 26 Oct 2022
A Linear Diophantine Equation | 3x+4y=17
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
published: 16 Mar 2023
Diophantine Equations: Strategies and Examples
This video is about Solving Diophantine Equations. Theory and Practice.
My merch: https://teespring.com/stores/sybermath?page=1
Follow me: https://twitter.com/SyberMath
Subscribe!!!: https://www.youtube.com/SyberMath?sub_confirmation=1
If you need to post a picture of your solution or idea:
https://twitter.com/intent/tweet?text=@SyberMath
#NumberTheoryProblems #DiophantineEquations
Chapters:
0:00 Introduction
1:18 Techniques
6:16 Problems
LINKS:
https://en.wikipedia.org/wiki/Diophantine_equation
https://www.math.uh.edu/~shanyuji/History/h-13a.pdf
https://www.britannica.com/biography/Diophantus
BOOKS:
https://www.amazon.com/Introduction-Diophantine-Equations-Problem-Based-Approach/dp/0817645489 (GREAT INTRO)
https://www.amazon.com/Diophantine-Equations-Pure-Applied-Mathematics/dp/012506...
published: 27 Jan 2021
Number Theory | Linear Diophantine Equations
We explore the solvability of the linear Diophantine equation ax+by=c
published: 28 Aug 2019
N1--Introduction to Linear Diophantine Equations
published: 12 Aug 2014
A Linear Diophantine Equation
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
published: 08 Mar 2023
Linear Diophantine Equations | Road to RSA Cryptography #3
This is the third video in a series of videos that leads up to the math of RSA Cryptography. This video series will cover the contents of the book "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" available here:
https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464
This content is covered in a Discrete Math course I often teach, and is usually covered in a stand alone Number Theory course at other institutions.
In this video we cover Linear Diophantine Equations. We give necessary and sufficient conditions for a linear diophantine equation to have integer solutions. We then characterize, for the linear diophantine equations that have solutions, a complete characterization of the entire solution set. This helps, for instance, with findi...
published: 18 May 2020
A Special Diophantine Equation in Number Theory with Special Formula You Need to Master
We are solving this nice diophantine equation and introducing a new trick you can use in order to solve a linear diophantine equation in algebra. This is a very simple but very useful trick you can use. Diophantine equation is a very important topic in algebra, and this video will guide you how to solve linear diophantine equation using this one particular and special skills and formulas. Make sure to watch the video until the end, and learn this trick for diophantine equation. This is a very nice diophantine equation. More to come! Stay tuned! Sharpen your algebra.
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media...
published: 06 Feb 2023
How to Solve a Three Variable Linear Diophantine Equation
In this video we examine two methods to solve a Linear Diophantine Equation in three variables. The first method is a general method which works with all of these types of questions, by first converting the equation to one in two variables, which we then solve by the method outlined in our previous video
'Solving Linear Diophantine Equations Using Euclid's Algorithm'
https://www.youtube.com/watch?v=t_a0PM02XeM&list=PLlX3COjsHPVBYydWJ2V4so1Fxd4Juq3nl&index=1
The second method only works in certain cases (when various of the coefficients have common factors), but uses modular maths and is a fun way to solve (assuming you think modular maths is fun, which I do).
For more videos on Diophantine Equations see our playlist 'Numbers and Number Theory'
https://www.youtube.com/playlist?list=PLlX3...
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 ...
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 show that you can solve the equation ax+by=GCD(a,b) by performing the Euclidean algorithm, and then reverse-substituting to arrive at a single solution.
Teacher: Michael Harrison
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: https://www.facebook.com/SocraticaStudios/
Instagram: https://www.instagram.com/SocraticaStudios/
Twitter: https://twitter.com/Socratica
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 show that you can solve the equation ax+by=GCD(a,b) by performing the Euclidean algorithm, and then reverse-substituting to arrive at a single solution.
Teacher: Michael Harrison
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: https://www.facebook.com/SocraticaStudios/
Instagram: https://www.instagram.com/SocraticaStudios/
Twitter: https://twitter.com/Socratica
In this video, I am introducing a nice diophantine equation in number theory and also a wonderful theorem you can use to solve a linear diophantine equation wit...
In this video, I am introducing a nice diophantine equation in number theory and also a wonderful theorem you can use to solve a linear diophantine equation with two unknown variables. With this theorem, most of the linear diophantine equations with two unknown variables will be nicely solved. Diophantine equation is an interesting topic in number theory. Come check this video out and watch it until the end. This would also be a good practice for math olympiad. More with diophantine equation problems will come! Stay tuned!
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ https://www.instagram.com/drpkmath1234/
Facebook ▶️ https://www.facebook.com/drpkmath
Twitter ▶️https://twitter.com/drpkmath
*************
#DrPKMath #diophantineequation #matholympiad
In this video, I am introducing a nice diophantine equation in number theory and also a wonderful theorem you can use to solve a linear diophantine equation with two unknown variables. With this theorem, most of the linear diophantine equations with two unknown variables will be nicely solved. Diophantine equation is an interesting topic in number theory. Come check this video out and watch it until the end. This would also be a good practice for math olympiad. More with diophantine equation problems will come! Stay tuned!
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ https://www.instagram.com/drpkmath1234/
Facebook ▶️ https://www.facebook.com/drpkmath
Twitter ▶️https://twitter.com/drpkmath
*************
#DrPKMath #diophantineequation #matholympiad
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@...
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
This video is about Solving Diophantine Equations. Theory and Practice.
My merch: https://teespring.com/stores/sybermath?page=1
Follow me: https://twitter.com/S...
This video is about Solving Diophantine Equations. Theory and Practice.
My merch: https://teespring.com/stores/sybermath?page=1
Follow me: https://twitter.com/SyberMath
Subscribe!!!: https://www.youtube.com/SyberMath?sub_confirmation=1
If you need to post a picture of your solution or idea:
https://twitter.com/intent/tweet?text=@SyberMath
#NumberTheoryProblems #DiophantineEquations
Chapters:
0:00 Introduction
1:18 Techniques
6:16 Problems
LINKS:
https://en.wikipedia.org/wiki/Diophantine_equation
https://www.math.uh.edu/~shanyuji/History/h-13a.pdf
https://www.britannica.com/biography/Diophantus
BOOKS:
https://www.amazon.com/Introduction-Diophantine-Equations-Problem-Based-Approach/dp/0817645489 (GREAT INTRO)
https://www.amazon.com/Diophantine-Equations-Pure-Applied-Mathematics/dp/0125062508 (MOST COMPREHENSIVE)
https://www.amazon.com/Diophantus-Diophantine-Equations-Mathematical-Expositions/dp/1470450488
https://www.amazon.com/Quadratic-Diophantine-Equations-Developments-Mathematics/dp/0387351566 (ADVANCED)
This video is about Solving Diophantine Equations. Theory and Practice.
My merch: https://teespring.com/stores/sybermath?page=1
Follow me: https://twitter.com/SyberMath
Subscribe!!!: https://www.youtube.com/SyberMath?sub_confirmation=1
If you need to post a picture of your solution or idea:
https://twitter.com/intent/tweet?text=@SyberMath
#NumberTheoryProblems #DiophantineEquations
Chapters:
0:00 Introduction
1:18 Techniques
6:16 Problems
LINKS:
https://en.wikipedia.org/wiki/Diophantine_equation
https://www.math.uh.edu/~shanyuji/History/h-13a.pdf
https://www.britannica.com/biography/Diophantus
BOOKS:
https://www.amazon.com/Introduction-Diophantine-Equations-Problem-Based-Approach/dp/0817645489 (GREAT INTRO)
https://www.amazon.com/Diophantine-Equations-Pure-Applied-Mathematics/dp/0125062508 (MOST COMPREHENSIVE)
https://www.amazon.com/Diophantus-Diophantine-Equations-Mathematical-Expositions/dp/1470450488
https://www.amazon.com/Quadratic-Diophantine-Equations-Developments-Mathematics/dp/0387351566 (ADVANCED)
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@...
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
This is the third video in a series of videos that leads up to the math of RSA Cryptography. This video series will cover the contents of the book "Number Theor...
This is the third video in a series of videos that leads up to the math of RSA Cryptography. This video series will cover the contents of the book "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" available here:
https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464
This content is covered in a Discrete Math course I often teach, and is usually covered in a stand alone Number Theory course at other institutions.
In this video we cover Linear Diophantine Equations. We give necessary and sufficient conditions for a linear diophantine equation to have integer solutions. We then characterize, for the linear diophantine equations that have solutions, a complete characterization of the entire solution set. This helps, for instance, with finding positive integer solutions to linear diophantine equations.
The book has many exercises that help students grasp the concept, and include problems like how to solve linear diophantine equations with three variables.
#LinearDiophantineEquations #EuclideanAlgorithm #RSACryptography
CHECK OUT OTHER TYPES OF VIDEOS:
================================
GRE Math Subject Test: https://www.youtube.com/playlist?list=PLBiVnG9A5gceFbk7oTBHALETI2SUmplIL
Putnam Math Competition: https://www.youtube.com/playlist?list=PLBiVnG9A5gcdLg0Im3qewDrgcMxpbjcqN
Math Theorem Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gccu9O8aCjVsynisfQLQyGOe
Math Problems Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gcc_1Kzd2xkHMXdO8zHz-W_4
Math Insights: https://www.youtube.com/playlist?list=PLBiVnG9A5gcfHRbtZcfQdJuUMAS6v48uj
Academic Advice: https://www.youtube.com/playlist?list=PLBiVnG9A5gce-PPdJQmtPNMsivAKKuXwe
GET MY BOOK ON AMAZON!!
========================
"Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures"
https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464
CHECK ME OUT ON THE INTERNET!!
==============================
TikTok: @profomarmath
Website: www.mohamedomar.org
Twitter: @ProfOmarMath
Instagram: profomarmath
YouTube: www.youtube.com/ProfOmarMath
And of course, subscribe to my channel!
This is the third video in a series of videos that leads up to the math of RSA Cryptography. This video series will cover the contents of the book "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" available here:
https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464
This content is covered in a Discrete Math course I often teach, and is usually covered in a stand alone Number Theory course at other institutions.
In this video we cover Linear Diophantine Equations. We give necessary and sufficient conditions for a linear diophantine equation to have integer solutions. We then characterize, for the linear diophantine equations that have solutions, a complete characterization of the entire solution set. This helps, for instance, with finding positive integer solutions to linear diophantine equations.
The book has many exercises that help students grasp the concept, and include problems like how to solve linear diophantine equations with three variables.
#LinearDiophantineEquations #EuclideanAlgorithm #RSACryptography
CHECK OUT OTHER TYPES OF VIDEOS:
================================
GRE Math Subject Test: https://www.youtube.com/playlist?list=PLBiVnG9A5gceFbk7oTBHALETI2SUmplIL
Putnam Math Competition: https://www.youtube.com/playlist?list=PLBiVnG9A5gcdLg0Im3qewDrgcMxpbjcqN
Math Theorem Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gccu9O8aCjVsynisfQLQyGOe
Math Problems Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gcc_1Kzd2xkHMXdO8zHz-W_4
Math Insights: https://www.youtube.com/playlist?list=PLBiVnG9A5gcfHRbtZcfQdJuUMAS6v48uj
Academic Advice: https://www.youtube.com/playlist?list=PLBiVnG9A5gce-PPdJQmtPNMsivAKKuXwe
GET MY BOOK ON AMAZON!!
========================
"Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures"
https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464
CHECK ME OUT ON THE INTERNET!!
==============================
TikTok: @profomarmath
Website: www.mohamedomar.org
Twitter: @ProfOmarMath
Instagram: profomarmath
YouTube: www.youtube.com/ProfOmarMath
And of course, subscribe to my channel!
We are solving this nice diophantine equation and introducing a new trick you can use in order to solve a linear diophantine equation in algebra. This is a very...
We are solving this nice diophantine equation and introducing a new trick you can use in order to solve a linear diophantine equation in algebra. This is a very simple but very useful trick you can use. Diophantine equation is a very important topic in algebra, and this video will guide you how to solve linear diophantine equation using this one particular and special skills and formulas. Make sure to watch the video until the end, and learn this trick for diophantine equation. This is a very nice diophantine equation. More to come! Stay tuned! Sharpen your algebra.
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ https://www.instagram.com/drpkmath1234/
Facebook ▶️ https://www.facebook.com/drpkmath
Twitter ▶️https://twitter.com/drpkmath
*************
#DrPKMath #diophantineequation #numbertheory #math #maths
We are solving this nice diophantine equation and introducing a new trick you can use in order to solve a linear diophantine equation in algebra. This is a very simple but very useful trick you can use. Diophantine equation is a very important topic in algebra, and this video will guide you how to solve linear diophantine equation using this one particular and special skills and formulas. Make sure to watch the video until the end, and learn this trick for diophantine equation. This is a very nice diophantine equation. More to come! Stay tuned! Sharpen your algebra.
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ https://www.instagram.com/drpkmath1234/
Facebook ▶️ https://www.facebook.com/drpkmath
Twitter ▶️https://twitter.com/drpkmath
*************
#DrPKMath #diophantineequation #numbertheory #math #maths
In this video we examine two methods to solve a Linear Diophantine Equation in three variables. The first method is a general method which works with all of the...
In this video we examine two methods to solve a Linear Diophantine Equation in three variables. The first method is a general method which works with all of these types of questions, by first converting the equation to one in two variables, which we then solve by the method outlined in our previous video
'Solving Linear Diophantine Equations Using Euclid's Algorithm'
https://www.youtube.com/watch?v=t_a0PM02XeM&list=PLlX3COjsHPVBYydWJ2V4so1Fxd4Juq3nl&index=1
The second method only works in certain cases (when various of the coefficients have common factors), but uses modular maths and is a fun way to solve (assuming you think modular maths is fun, which I do).
For more videos on Diophantine Equations see our playlist 'Numbers and Number Theory'
https://www.youtube.com/playlist?list=PLlX3COjsHPVA30n752HYKa3oRJI-QygWO
For more videos on Advanced Equation Solving see our playlist 'Advanced Equation Solving'
https://www.youtube.com/playlist?list=PLlX3COjsHPVBYydWJ2V4so1Fxd4Juq3nl
For more JEE Aspirant videos see our playlist 'JEE Aspirants'
https://www.youtube.com/playlist?list=PLlX3COjsHPVAyTDuUPm9jQy6LtI4-KcHg
In this video we examine two methods to solve a Linear Diophantine Equation in three variables. The first method is a general method which works with all of these types of questions, by first converting the equation to one in two variables, which we then solve by the method outlined in our previous video
'Solving Linear Diophantine Equations Using Euclid's Algorithm'
https://www.youtube.com/watch?v=t_a0PM02XeM&list=PLlX3COjsHPVBYydWJ2V4so1Fxd4Juq3nl&index=1
The second method only works in certain cases (when various of the coefficients have common factors), but uses modular maths and is a fun way to solve (assuming you think modular maths is fun, which I do).
For more videos on Diophantine Equations see our playlist 'Numbers and Number Theory'
https://www.youtube.com/playlist?list=PLlX3COjsHPVA30n752HYKa3oRJI-QygWO
For more videos on Advanced Equation Solving see our playlist 'Advanced Equation Solving'
https://www.youtube.com/playlist?list=PLlX3COjsHPVBYydWJ2V4so1Fxd4Juq3nl
For more JEE Aspirant videos see our playlist 'JEE Aspirants'
https://www.youtube.com/playlist?list=PLlX3COjsHPVAyTDuUPm9jQy6LtI4-KcHg
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 show that you can solve the equation ax+by=GCD(a,b) by performing the Euclidean algorithm, and then reverse-substituting to arrive at a single solution.
Teacher: Michael Harrison
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: https://www.facebook.com/SocraticaStudios/
Instagram: https://www.instagram.com/SocraticaStudios/
Twitter: https://twitter.com/Socratica
In this video, I am introducing a nice diophantine equation in number theory and also a wonderful theorem you can use to solve a linear diophantine equation with two unknown variables. With this theorem, most of the linear diophantine equations with two unknown variables will be nicely solved. Diophantine equation is an interesting topic in number theory. Come check this video out and watch it until the end. This would also be a good practice for math olympiad. More with diophantine equation problems will come! Stay tuned!
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ https://www.instagram.com/drpkmath1234/
Facebook ▶️ https://www.facebook.com/drpkmath
Twitter ▶️https://twitter.com/drpkmath
*************
#DrPKMath #diophantineequation #matholympiad
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
This video is about Solving Diophantine Equations. Theory and Practice.
My merch: https://teespring.com/stores/sybermath?page=1
Follow me: https://twitter.com/SyberMath
Subscribe!!!: https://www.youtube.com/SyberMath?sub_confirmation=1
If you need to post a picture of your solution or idea:
https://twitter.com/intent/tweet?text=@SyberMath
#NumberTheoryProblems #DiophantineEquations
Chapters:
0:00 Introduction
1:18 Techniques
6:16 Problems
LINKS:
https://en.wikipedia.org/wiki/Diophantine_equation
https://www.math.uh.edu/~shanyuji/History/h-13a.pdf
https://www.britannica.com/biography/Diophantus
BOOKS:
https://www.amazon.com/Introduction-Diophantine-Equations-Problem-Based-Approach/dp/0817645489 (GREAT INTRO)
https://www.amazon.com/Diophantine-Equations-Pure-Applied-Mathematics/dp/0125062508 (MOST COMPREHENSIVE)
https://www.amazon.com/Diophantus-Diophantine-Equations-Mathematical-Expositions/dp/1470450488
https://www.amazon.com/Quadratic-Diophantine-Equations-Developments-Mathematics/dp/0387351566 (ADVANCED)
⭐ Join this channel to get access to perks:
https://www.youtube.com/channel/UCW4czokv40JYR-w7u6aXZ3g/join
⭐SUBSCRIBE to MAIN CHANNEL → https://www.youtube.com/@SyberMath?sub_confirmation=1
⭐ SUBSCRIBE to SHORTS Channel → https://www.youtube.com/@SyberMathShorts?sub_confirmation=1
⭐Follow me → https://twitter.com/SyberMath
#shorts #shortsvideo #shortsyoutube
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva
This is the third video in a series of videos that leads up to the math of RSA Cryptography. This video series will cover the contents of the book "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" available here:
https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464
This content is covered in a Discrete Math course I often teach, and is usually covered in a stand alone Number Theory course at other institutions.
In this video we cover Linear Diophantine Equations. We give necessary and sufficient conditions for a linear diophantine equation to have integer solutions. We then characterize, for the linear diophantine equations that have solutions, a complete characterization of the entire solution set. This helps, for instance, with finding positive integer solutions to linear diophantine equations.
The book has many exercises that help students grasp the concept, and include problems like how to solve linear diophantine equations with three variables.
#LinearDiophantineEquations #EuclideanAlgorithm #RSACryptography
CHECK OUT OTHER TYPES OF VIDEOS:
================================
GRE Math Subject Test: https://www.youtube.com/playlist?list=PLBiVnG9A5gceFbk7oTBHALETI2SUmplIL
Putnam Math Competition: https://www.youtube.com/playlist?list=PLBiVnG9A5gcdLg0Im3qewDrgcMxpbjcqN
Math Theorem Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gccu9O8aCjVsynisfQLQyGOe
Math Problems Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gcc_1Kzd2xkHMXdO8zHz-W_4
Math Insights: https://www.youtube.com/playlist?list=PLBiVnG9A5gcfHRbtZcfQdJuUMAS6v48uj
Academic Advice: https://www.youtube.com/playlist?list=PLBiVnG9A5gce-PPdJQmtPNMsivAKKuXwe
GET MY BOOK ON AMAZON!!
========================
"Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures"
https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464
CHECK ME OUT ON THE INTERNET!!
==============================
TikTok: @profomarmath
Website: www.mohamedomar.org
Twitter: @ProfOmarMath
Instagram: profomarmath
YouTube: www.youtube.com/ProfOmarMath
And of course, subscribe to my channel!
We are solving this nice diophantine equation and introducing a new trick you can use in order to solve a linear diophantine equation in algebra. This is a very simple but very useful trick you can use. Diophantine equation is a very important topic in algebra, and this video will guide you how to solve linear diophantine equation using this one particular and special skills and formulas. Make sure to watch the video until the end, and learn this trick for diophantine equation. This is a very nice diophantine equation. More to come! Stay tuned! Sharpen your algebra.
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
https://www.youtube.com/c/DrPKMath?sub_confirmation=1
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ https://www.instagram.com/drpkmath1234/
Facebook ▶️ https://www.facebook.com/drpkmath
Twitter ▶️https://twitter.com/drpkmath
*************
#DrPKMath #diophantineequation #numbertheory #math #maths
In this video we examine two methods to solve a Linear Diophantine Equation in three variables. The first method is a general method which works with all of these types of questions, by first converting the equation to one in two variables, which we then solve by the method outlined in our previous video
'Solving Linear Diophantine Equations Using Euclid's Algorithm'
https://www.youtube.com/watch?v=t_a0PM02XeM&list=PLlX3COjsHPVBYydWJ2V4so1Fxd4Juq3nl&index=1
The second method only works in certain cases (when various of the coefficients have common factors), but uses modular maths and is a fun way to solve (assuming you think modular maths is fun, which I do).
For more videos on Diophantine Equations see our playlist 'Numbers and Number Theory'
https://www.youtube.com/playlist?list=PLlX3COjsHPVA30n752HYKa3oRJI-QygWO
For more videos on Advanced Equation Solving see our playlist 'Advanced Equation Solving'
https://www.youtube.com/playlist?list=PLlX3COjsHPVBYydWJ2V4so1Fxd4Juq3nl
For more JEE Aspirant videos see our playlist 'JEE Aspirants'
https://www.youtube.com/playlist?list=PLlX3COjsHPVAyTDuUPm9jQy6LtI4-KcHg
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integersolutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. An exponential Diophantine equation is one in which exponents on terms can be unknowns.
Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, and ask about the lattice points on it.
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.
The intellectuals of ancient Alexandria had a profound impact on several disciplines. PhotoCredits. Mr. D. B. Goswami ... Photo Credits. Mr. Arunansh B. Goswami ... Photo Credits. Mr. D ... Diophantus also worked with equations, now referred to as Diophantine equations.
Anyone who regularly uses the London Underground in the summer will attest to the baking heat and sweltering conditions. Pictured ... Your commute is probably already stressful enough without having to solve the Tube equivalent of a Diophantine equation ... .
Anyone who regularly uses the London Underground in the summer will attest to the baking heat and sweltering conditions. Pictured ... Your commute is probably already stressful enough without having to solve the Tube equivalent of a Diophantine equation ... .