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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a linear congruence?
💡 Hint: Think about what happens in usual algebra with variables.
Question 2
Easy
State the Chinese Remainder Theorem.
💡 Hint: Consider how multiple conditions can coexist.
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: Focus on the equation format and its components.
Question 2
True or False: The Chinese Remainder Theorem guarantees multiple solutions in the range of moduli.
- True
- False
💡 Hint: Consider what 'unique' means in this context.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that for any integers a, b, and N, if GCD(a, N) = d > 1, then the linear congruence ax ≡ b mod N has either no solutions or infinitely many solutions.
💡 Hint: Consider factors and multiples involved in the equation.
Question 2
Using the Extended Euclidean Algorithm, find the solutions x for the congruence 15x ≡ 3 mod 30.
💡 Hint: Reduce the congruence to simpler terms using the GCD.
Challenge and get performance evaluation