Practice Uniqueness Proof Part for the Chinese Remainder Theorem - 11.2.3 | 11. Uniqueness Proof of the CRT | Discrete Mathematics - Vol 3
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11.2.3 - Uniqueness Proof Part for the Chinese Remainder Theorem

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Explain Euclid's Lemma in your own words.

💡 Hint: Think of how primes work with products.

Question 2

Easy

What does it mean for numbers to be 'pairwise relatively prime'?

💡 Hint: Look at pairs of numbers and their factors.

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 a product of integers if it divides each integer separately.
  • A prime divides a product of integers if it divides at least one of the integers.
  • A prime only divides even integers.

💡 Hint: Think of how primes operate in multiplication.

Question 2

True or False: If a system of linear congruences has more than one solution, they must be congruent modulo M.

  • True
  • False

💡 Hint: Consider the implications of congruence properties.

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Challenge Problems

Push your limits with challenges.

Question 1

Given three integers 4, 6, and 10, demonstrate using CRT that a linear combination of these can yield a unique solution within a defined modulus that is their product.

💡 Hint: Break down each modulus and product relation carefully.

Question 2

Suppose there are solutions x1 and x2 for a given set of linear equations. Show that if these solutions yield differing results, it contradicts the uniqueness principle established in CRT.

💡 Hint: Bring in the notion of divisibility and modulo relations.

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