11.2.1 - Properties of Divisibility
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Practice Questions
Test your understanding with targeted questions
What does Bezout's theorem state?
💡 Hint: Think about expressing GCD in terms of a linear combination.
What does Euclid's lemma suggest about prime numbers?
💡 Hint: Consider prime factors when multiplying numbers.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Bezout's theorem relate to?
💡 Hint: Look for the theorem's key term.
True or False: Euclid's lemma states a prime must divide all factors in a product.
💡 Hint: Remember its definition regarding primes.
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Challenge Problems
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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.
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.
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