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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what it means for a number p to be prime.
💡 Hint: Consider the smallest prime examples.
Question 2
Easy
What does it mean if p divides a product of numbers?
💡 Hint: Think about factors of numbers.
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?
- A prime divides all products
- A prime divides at least one factor of a product
- None of the above
💡 Hint: Review the definition of primes.
Question 2
True or False: If p divides ab, then p must also divide a.
- True
- False
💡 Hint: Think about counterexamples.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove by induction that if a prime divides a product of any n integers, it divides at least one of those integers.
💡 Hint: Focus on how the prime interacts with the product.
Question 2
Using Euclid's Lemma, show why it implies that any solution to a system of linear congruences in CRT must be unique.
💡 Hint: Assess the implications of congruences.
Challenge and get performance evaluation