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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: Divide both sides by 2 after checking GCD.
Question 2
Easy
If 5x ≡ 10 (mod 15), what are possible values of x?
💡 Hint: What happens when you divide both sides by 5?
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 a and N to be coprime when solving linear congruences?
- They share a common divisor.
- Their GCD is 1.
- They are both even.
💡 Hint: Recall the definition of coprime.
Question 2
True or False: Every linear congruence has a unique solution.
- True
- False
💡 Hint: Consider the structure of modular arithmetic.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given five different congruences x ≡ 1 (mod 5), x ≡ 2 (mod 6), x ≡ 3 (mod 7), x ≡ 4 (mod 8), and x ≡ 5 (mod 9), determine the unique solution modulo the product of these moduli.
💡 Hint: Start solving each congruence stepwise using pairwise relationships.
Question 2
Find the multiplicative inverse of 15 modulo 26. Show each step.
💡 Hint: Remember the steps to apply the algorithm carefully.
Challenge and get performance evaluation