Practice Euclid’s Lemma (11.2.2) - Uniqueness Proof of the CRT - Discrete Mathematics

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6 sample questions

Question 1.
Define what it means for a number p to be prime.
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Consider the smallest prime examples.
Question 2.
What does it mean if p divides a product of numbers?
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Think about factors of numbers.
3Question 3.
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
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Review the definition of primes.
4Question 4.
True or False: If p divides ab, then p must also divide a.
- True
- False
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Think about counterexamples.
Question 5.
Prove by induction that if a prime divides a product of any n integers, it divides at least one of those integers.
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Focus on how the prime interacts with the product.
Question 6.
Using Euclid's Lemma, show why it implies that any solution to a system of linear congruences in CRT must be unique.
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Assess the implications of congruences.

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