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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a linear congruence? Provide an example.
💡 Hint: Look for the standard form.
Question 2
Easy
How many solutions does the linear congruence 4x ≡ 8 (mod 12) have?
💡 Hint: Consider all values that satisfy the equation.
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 a linear congruence?
💡 Hint: Think of modular arithmetic.
Question 2
True or False: The Chinese Remainder Theorem guarantees multiple solutions for all systems of linear congruences.
- True
- False
💡 Hint: Recall the uniqueness condition.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find all integer solutions for the system: x ≡ 1 (mod 4), x ≡ 3 (mod 5), and x ≡ 2 (mod 7).
💡 Hint: Start with calculating the larger modulus.
Question 2
Determine the implications of changing one modulus in a set of congruences. For instance, replace mod 5 with mod 6.
💡 Hint: Evaluate how congruences relate to divisibility.
Challenge and get performance evaluation