11.2.2 - Euclid’s Lemma
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Practice Questions
Test your understanding with targeted questions
Define what it means for a number p to be prime.
💡 Hint: Consider the smallest prime examples.
What does it mean if p divides a product of numbers?
💡 Hint: Think about factors of numbers.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Euclid's Lemma state?
💡 Hint: Review the definition of primes.
True or False: If p divides ab, then p must also divide a.
💡 Hint: Think about counterexamples.
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Challenge Problems
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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.
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.
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