1.2 - Properties of the Order of a Finite Field
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Practice Questions
Test your understanding with targeted questions
What is the order of the finite field ℤ5?
💡 Hint: Recall that the order is the number of elements.
What is meant by the characteristic of a finite field?
💡 Hint: Think about addition within the field.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the order of a finite field with characteristic 7?
💡 Hint: Think about prime powers.
True or False: The characteristic of a finite field can be a composite number.
💡 Hint: Consider what defines a field.
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Challenge Problems
Push your limits with advanced challenges
Construct a finite field with characteristic 3 and of order 3^2.
💡 Hint: Make sure your polynomial cannot be factored over ℤ.
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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