The Chinese Remainder Theorem - In About 17 Minutes | Number Theory | Abstract Algebra

Solve a system of congruences with the Chinese Remainder Theorem. We restate CRT, check the gcd condition, convert each congruence to equations, solve the resulting linear Diophantine equation with the Extended Euclidean Algorithm matrix method, compute the least common multiple, and verify the final solution. You will see how x ≡ 3415 (mod 4662) satisfies x ≡ 11 (mod 74) and x ≡ 13 (mod 63), and how to write all solutions. https://youtu.be/8Ah9xMQm6jI https://youtu.be/kGv8LSyO6YQ https://www.youtube.com/playlist?list=PLm90IN9RVLf93O1-8jFXL62M8gnFO-Rsd https://www.youtube.com/playlist?list=PLm90IN9RVLf9hn9po3pPHzK540MCY6XMY https://www.youtube.com/playlist?list=PLm90IN9RVLf8tKoCjzsg8W1Td_72KaTeY https://www.youtube.com/playlist?list=PLm90IN9RVLf_BneWC40564ZZAqpe2sz6- Chapters: 00:00 Introduction 01:15 Chinese Remainder Theorem 02:36 Example 03:07 Euclidean Algorithm 05:12 Rewrite Congruences as Equations 06:26 Linear Diophantine Equation and EEA Matrix 12:01 Particular Solution for x 12:53 Least Common Multiple 15:11 Verification 16:20 General Solution form and Thanks for Watching #dogmathic #Mathematics #highermath #numbertheory #abstractalgebra #chineseremaindertheorem #crt #discrete_mathematics #modulararithmetic #Congruences #EuclideanAlgorithm #ExtendedEuclidean #Diophantine #CRT