Practice Bezout’s Theorem - 9.2 | 9. Lecture – 57: Properties of GCD and Bezout’s Theorem | Discrete Mathematics - Vol 3
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9.2 - Bezout’s Theorem

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is Bezout's Theorem?

💡 Hint: Think about how GCD relates to other integer properties.

Question 2

Easy

How do you express a linear combination?

💡 Hint: Recall the defining equation involving GCD.

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 Bezout's theorem state?

  • The GCD is always positive
  • The GCD can be expressed as a linear combination of its integers
  • The GCD is always an integer

💡 Hint: Recall the relationship between GCD and linear combinations.

Question 2

True or False: If two integers are co-prime, their GCD is 1.

  • True
  • False

💡 Hint: Think about the definition of co-prime.

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Challenge Problems

Push your limits with challenges.

Question 1

Use the extended Euclidean algorithm to find the GCD of 57 and 34. Express the GCD as a linear combination using Bezout's coefficients.

💡 Hint: Track remainders and apply backward substitution.

Question 2

Determine if the integer 45 has a multiplicative inverse under modulo 64 and explain your reasoning.

💡 Hint: Check the GCD result to confirm if an inverse exists.

Challenge and get performance evaluation