Master the Chinese Remainder Theorem in Just 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.

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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

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