Practice Summary of Today's Lecture - 10.10 | 10. Linear Congruence Equations and Chinese Remainder Theorem | Discrete Mathematics - Vol 3
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Summary of Today's Lecture

10.10 - Summary of Today's Lecture

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Practice Questions

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Question 1 Easy

What is the solution for the linear congruence 4x ≡ 2 (mod 6)?

💡 Hint: Use the concept of divisibility in modular arithmetic.

Question 2 Easy

How do you express solutions for 3x ≡ 1 (mod 8)?

💡 Hint: Find an integer such that `3 * ? ≡ 1 (mod 8)`.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the general solution format for 6x ≡ 4 (mod 10)?

x = 4 + 10k
x = 5 + 10k
x = 3 + 10k

💡 Hint: Think about how the solution can be expressed with `k` integer.

Question 2

True or False: The Extended Euclidean Algorithm can be applied if gcd(a, N) is greater than 1.

True
False

💡 Hint: Recall the conditions for the applicability of this algorithm.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Solve the following system using the Chinese Remainder Theorem: x ≡ 4 (mod 5), x ≡ 1 (mod 3), x ≡ 2 (mod 7). Provide full steps in your reasoning.

💡 Hint: Start by calculating the product of moduli.

Challenge 2 Hard

Employ the Extended Euclidean Algorithm to find the multiplicative inverse of 7 mod 26. Show your steps.

💡 Hint: Remember the last non-zero remainder should give you the gcd proof.

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