Practice Existence of Multiplicative Inverse - 9.6 | 9. Lecture – 57: Properties of GCD and Bezout’s Theorem | Discrete Mathematics - Vol 3
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Existence of Multiplicative Inverse

9.6 - Existence of Multiplicative Inverse

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define what a multiplicative inverse is.

💡 Hint: Think about what it means to reverse a multiplication.

Question 2 Easy

What condition must be met for a multiplicative inverse to exist?

💡 Hint: Look at the relationship expressed by Bezout's theorem.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the multiplicative inverse of 3 modulo 7?

1
2
5

💡 Hint: Try multiplying 3 with each option and see if the result is 1.

Question 2

True or False: A multiplicative inverse exists if GCD(a, N) = 0.

True
False

💡 Hint: Remember the GCD’s role in determining co-primality.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Find the multiplicative inverse of 11 modulo 31 using the Extended Euclidean Algorithm.

💡 Hint: Utilize the extended algorithm step-by-step to find the necessary coefficients.

Challenge 2 Hard

Explain in detail why the existence of a multiplicative inverse is essential in RSA algorithm applications.

💡 Hint: Consider how the keys relate to modular arithmetic operations.

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