Practice Proof of Bezout’s Theorem - 9.3 | 9. Lecture – 57: Properties of GCD and Bezout’s Theorem | Discrete Mathematics - Vol 3
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

9.3 - Proof of Bezout’s Theorem

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does Bezout's Theorem state?

💡 Hint: Think about relationships between two integers.

Question 2

Easy

Define the term GCD.

💡 Hint: Consider what it means to evenly divide a number.

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 the main assertion of Bezout's Theorem?

  • GCD can be expressed as multiplication
  • GCD can be expressed as a linear combination
  • GCD cannot be expressed

💡 Hint: Think about how GCD relates to linear equations.

Question 2

True or False: The Extended Euclidean Algorithm finds the GCD and integer coefficients.

  • True
  • False

💡 Hint: Consider the main functions of the Extended Euclidean Algorithm.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Use integers a = 84 and b = 30. Find the GCD using both the Euclidean and Extended Euclidean methods, providing s and t.

💡 Hint: Iterate through finding remainders until you reach zero.

Question 2

Suppose a and b are both even integers. Prove that their GCD is even using the principles from Bezout’s Theorem.

💡 Hint: Consider the implications of linear combinations in your proof.

Challenge and get performance evaluation