9.3 - Proof of Bezout’s Theorem
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Practice Questions
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What does Bezout's Theorem state?
💡 Hint: Think about relationships between two integers.
Define the term GCD.
💡 Hint: Consider what it means to evenly divide a number.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main assertion of Bezout's Theorem?
💡 Hint: Think about how GCD relates to linear equations.
True or False: The Extended Euclidean Algorithm finds the GCD and integer coefficients.
💡 Hint: Consider the main functions of the Extended Euclidean Algorithm.
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Challenge Problems
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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.
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.
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