Practice Application of Chinese Remainder Theorem - 11.2.6 | 11. Uniqueness Proof of the CRT | Discrete Mathematics - Vol 3
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11.2.6 - Application of Chinese Remainder Theorem

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the Chinese Remainder Theorem?

💡 Hint: Consider its relation to moduli.

Question 2

Easy

Define coprime numbers.

💡 Hint: Think of prime 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 is guaranteed by the Chinese Remainder Theorem?

  • No solution exists
  • A unique solution exists
  • Multiple solutions exist

💡 Hint: Think about the uniqueness in systems of equations.

Question 2

True or False: If two numbers are congruent mod m and m is prime, they are equal.

  • True
  • False

💡 Hint: Consider the possibilities outside of congruence.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Prove that the CRT can be extended to more than two moduli.

💡 Hint: Think about the relationships of congruences.

Question 2

If 17 and 19 are coprime moduli, find a number less than 323 that is congruent to 5 mod 17 and congruent to 12 mod 19.

💡 Hint: Calculate the respective products and their inverses.

Challenge and get performance evaluation