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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What are the conditions under which a linear congruence has a unique solution?
💡 Hint: What do we mean by the coefficients being coprime?
Question 2
Easy
Solve the linear congruence 4x ≡ 2 (mod 6).
💡 Hint: Check if a and n share common factors.
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 does it mean for two numbers to be coprime?
- They have no common divisors
- They are equal
- They are both prime
💡 Hint: Think about the GCD definition.
Question 2
True or False: The Chinese Remainder Theorem can find solutions for any moduli.
- True
- False
💡 Hint: Consider the requirements for CRT to work.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Solve the system of congruences: x ≡ 1 (mod 2), x ≡ 2 (mod 3), x ≡ 3 (mod 4). Show your work and verify all solutions.
💡 Hint: Break down each congruence systematically.
Question 2
Apply the Extended Euclidean Algorithm to determine the inverse of 14 modulo 33, then solve 14x ≡ 11 (mod 33).
💡 Hint: Look for steps in the algorithm outlining the GCD.
Challenge and get performance evaluation