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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does Bezout's theorem state?
💡 Hint: Think about expressing GCD in terms of a linear combination.
Question 2
Easy
What does Euclid's lemma suggest about prime numbers?
💡 Hint: Consider prime factors when multiplying 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 Bezout's theorem relate to?
- Prime Factorization
- GCD
- Division
💡 Hint: Look for the theorem's key term.
Question 2
True or False: Euclid's lemma states a prime must divide all factors in a product.
- True
- False
💡 Hint: Remember its definition regarding primes.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove the uniqueness of the solution in CRT when given two congruences a ≡ x (mod m) and b ≡ x (mod n) with m and n coprime.
💡 Hint: Use the properties we discussed in specifics.
Question 2
Using a set of numbers with primes, prove that for any number k, if p divides the product of k numbers, p must divide at least one number.
💡 Hint: Break it down with induction steps.
Challenge and get performance evaluation