Practice Existence of Multiplicative Inverse - 1.11 | Overview 41 | Discrete Mathematics - Vol 3
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the characteristic of a finite field?

💡 Hint: Think about how often you need to add 1 before you get 0.

Question 2

Easy

Define a multiplicative inverse.

💡 Hint: Can you think of any examples of such elements?

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 characteristic of a finite field?

  • A prime number
  • Any integer
  • Only even integers

💡 Hint: Remember that characteristics involve addition leading to zero.

Question 2

True or False: Every non-zero element in a finite field has a unique multiplicative inverse.

  • True
  • False

💡 Hint: Think about the definitions we've discussed.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a finite field with characteristic 5, find the order of the field if r = 3. Prove the validity of your answer.

💡 Hint: Remember the form pr for field order.

Question 2

Construct a finite field from the polynomial x^2 + 1 over GF(3). Identify all elements and calculate the multiplicative inverse of 2.

💡 Hint: Utilize the polynomial to generate elements and assess their relationships.

Challenge and get performance evaluation