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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean for a number 'a' to divide 'b'?
💡 Hint: Think about the division operation.
Question 2
Easy
State Euclid's Lemma in your own words.
💡 Hint: Relate it to an example you’ve seen.
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 Euclid’s Lemma state?
- p divides the product implies p divides none of them
- p divides the product implies p divides at least one of them
- p is always greater than one
💡 Hint: Think about how prime factors interact with products.
Question 2
True or False: The Helping Lemma assures the existence of unique solutions in CRT.
- True
- False
💡 Hint: Remember the implications of congruences and moduli.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the congruences x ≡ 3 mod 4, x ≡ 4 mod 5, and x ≡ 2 mod 6, find all possible values of x.
💡 Hint: You must consider each modulus and their pairwise relations.
Question 2
Demonstrate why the Chinese Remainder Theorem cannot work if the moduli are not pairwise coprime, with a specific example.
💡 Hint: Think about divisibility and overlap in factors.
Challenge and get performance evaluation