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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the GCD of 12 and 15?
💡 Hint: Find the largest integer that divides both numbers.
Question 2
Easy
Can you express the GCD of 8 and 12 as a linear combination?
💡 Hint: Use integer coefficients to represent the combination.
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 of two integers can be expressed as a product.
- The GCD of two integers can be expressed as a linear combination.
- The GCD is always a prime number.
💡 Hint: Think about how we discussed expressing the GCD.
Question 2
True or False: The coefficients in Bezout's theorem are always positive.
- True
- False
💡 Hint: Consider the examples we went through.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if a is a multiple of N, then it cannot have a multiplicative inverse modulo N.
💡 Hint: Consider the definition of GCD.
Question 2
Use the Extended Euclidean Algorithm to find the GCD of 101 and 10, and express it using Bezout's coefficients.
💡 Hint: Document each step in the algorithm carefully.
Challenge and get performance evaluation