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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does the notation a ≡ b (mod N) mean?
💡 Hint: Think about the definition of congruence.
Question 2
Easy
If x ≡ 3 (mod 5), what could be a value of x?
💡 Hint: Find such numbers by adding multiples of 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 is the condition for using the extended Euclidean algorithm?
- GCD(a
- N) = 1
- GCD(a
- N) > 1
- a and N are both 0
💡 Hint: What condition does the existence of an inverse require?
Question 2
True or False: The Chinese Remainder Theorem guarantees a unique solution for any set of congruences.
- True
- False
💡 Hint: Think about the conditions of the theorems discussed.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using the Chinese Remainder Theorem, solve for x in the system: x ≡ 1 (mod 4), x ≡ 3 (mod 5), x ≡ 2 (mod 7).
💡 Hint: Determine the product of moduli and work through the steps of CRT.
Question 2
Show that x ≡ 5 (mod 15) has infinitely many solutions, and list at least three.
💡 Hint: Use the general formula for solutions in linear congruences.
Challenge and get performance evaluation