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Practice Questions
Test your understanding with targeted questions related to the topic.
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)`.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
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.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation