10.10 - Summary of Today's Lecture
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.
Practice Questions
Test your understanding with targeted questions
What is the solution for the linear congruence 4x ≡ 2 (mod 6)?
💡 Hint: Use the concept of divisibility in modular arithmetic.
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
What is the general solution format for 6x ≡ 4 (mod 10)?
💡 Hint: Think about how the solution can be expressed with `k` integer.
True or False: The Extended Euclidean Algorithm can be applied if gcd(a, N) is greater than 1.
💡 Hint: Recall the conditions for the applicability of this algorithm.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.