22.2 - Verification of Field Axioms
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Practice Questions
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What is the characteristic of a finite field?
💡 Hint: Think about how many times you can add 1 to reach 0.
What is an irreducible polynomial?
💡 Hint: Consider the definitions of factorization.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the characteristic of a finite field?
💡 Hint: Consider the definition of characteristic.
True or False: An irreducible polynomial can be factored into simpler polynomials.
💡 Hint: Think about what 'irreducible' implies.
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Challenge Problems
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Prove that if you have a finite field with characteristic p, where p is prime, can you show that there are no non-trivial divisors of p?
💡 Hint: Review the definition of prime numbers.
Given an irreducible polynomial of degree 2, how would you construct a finite field using it?
💡 Hint: Recall the construction process we discussed in class.
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