Discrete Mathematics - Vol 3 | 10. Linear Congruence Equations and Chinese Remainder Theorem by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge
10. Linear Congruence Equations and Chinese Remainder Theorem

Linear congruences and their solutions can be effectively understood through two methods: the extended Euclidean algorithm and the Chinese Remainder Theorem (CRT). The chapter introduces linear congruences as an extension of linear equations into modular arithmetic, showcasing methods to find solutions under given conditions. Ultimately, it emphasizes the significance of finding unique solutions within a specified range, thus establishing a foundational understanding of linear congruences in discrete mathematics.

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

  • 10

    Linear Congruence Equations And Chinese Remainder Theorem

    This section introduces linear congruences and two methods for solving them: the extended Euclid’s algorithm and the Chinese Remainder Theorem.

    Learning Practice

  • 10.1

    Introduction To Linear Congruences

    This section introduces linear congruences, detailing methods for their solution, including the Extended Euclidean Algorithm and the Chinese Remainder Theorem.

    Learning Practice

  • 10.2

    Solving Linear Congruences Using Extended Euclid's Algorithm

    This section introduces linear congruences and explains two methods for solving them, focusing on the extended Euclid's algorithm and the Chinese Remainder Theorem.

    Learning Practice

  • 10.3

    Chinese Remainder Theorem (Crt)

    The section introduces linear congruence equations and presents two methods for solving them: the extended Euclid's algorithm and the Chinese Remainder Theorem.

    Learning Practice

  • 10.4

    Statement Of The Chinese Remainder Theorem

    This section introduces the Chinese Remainder Theorem (CRT) and its application in solving systems of linear congruences.

    Learning Practice

  • 10.5

    Proof Strategy For Chinese Remainder Theorem

    This section introduces the concept of linear congruences and the Chinese Remainder Theorem (CRT), showcasing methods for solving systems of linear congruences.

    Learning Practice

  • 10.6

    Finding A Special Linear Combination For The Solution

    This section introduces linear congruences and discusses methods for solving them, specifically the extended Euclidean algorithm and the Chinese Remainder Theorem (CRT).

    Learning Practice

  • 10.7

    Construction Of The Solution X

    This section focuses on solving linear congruences using two methods: the Extended Euclid's algorithm and the Chinese Remainder Theorem (CRT).

    Learning Practice

  • 10.8

    Verifying The Solution

    This section explores methods for solving linear congruences using the extended Euclid’s algorithm and the Chinese Remainder Theorem (CRT), emphasizing the verification of solutions.

    Learning Practice

  • 10.9

    Finding Solutions In A Specific Range

    This section introduces methods for solving linear congruences using the Extended Euclidean Algorithm and the Chinese Remainder Theorem (CRT).

    Learning Practice

  • 10.10

    Summary Of Today's Lecture

    This section provides an overview of linear congruences and methods for solving them, particularly focusing on the Extended Euclidean Algorithm and the Chinese Remainder Theorem.

    Learning Practice

References

ch59.pdf

Class Notes

Memorization

What we have learnt

  • Linear congruences extend t...
  • The extended Euclidean algo...
  • The Chinese Remainder Theor...

Final Test

Revision Tests