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

9.2 - Bezout’s Theorem

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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