Practice Proof Of Bezout’s Theorem (9.3) - Lecture – 57: Properties of GCD and Bezout’s Theorem

Practice: Proof of Bezout’s Theorem

Lesson 9.3Lecture – 57: Properties of GCD and Bezout’s Theorem

Practise this section

9 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What does Bezout's Theorem state?
Show hintHide hint
Think about relationships between two integers.
Question 2.
Define the term GCD.
Show hintHide hint
Consider what it means to evenly divide a number.
3Question 3.
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
Show hintHide hint
Think about how GCD relates to linear equations.
4Question 4.
True or False: The Extended Euclidean Algorithm finds the GCD and integer coefficients.
- True
- False
Show hintHide hint
Consider the main functions of the Extended Euclidean Algorithm.
Question 5.
Use integers a = 84 and b = 30. Find the GCD using both the Euclidean and Extended Euclidean methods, providing s and t.
Show hintHide hint
Iterate through finding remainders until you reach zero.
Question 6.
Suppose a and b are both even integers. Prove that their GCD is even using the principles from Bezout’s Theorem.
Show hintHide hint
Consider the implications of linear combinations in your proof.

5 more questions in this section. Enroll free to practise them all.