Practice Properties of the Order of a Finite Field - 1.2 | Overview 41 | Discrete Mathematics - Vol 3
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Properties of the Order of a Finite Field

1.2 - Properties of the Order of a Finite Field

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the order of the finite field ℤ5?

💡 Hint: Recall that the order is the number of elements.

Question 2 Easy

What is meant by the characteristic of a finite field?

💡 Hint: Think about addition within the field.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the order of a finite field with characteristic 7?

7
14
7^2

💡 Hint: Think about prime powers.

Question 2

True or False: The characteristic of a finite field can be a composite number.

True
False

💡 Hint: Consider what defines a field.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Construct a finite field with characteristic 3 and of order 3^2.

💡 Hint: Make sure your polynomial cannot be factored over ℤ.

Challenge 2 Hard

Show that the mapping from ℤr(p) to F is a bijection.

💡 Hint: Use definitions of injectivity and surjectivity to support your argument.

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Reference links

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