Practice Proof Of The Theorem (1.3) - Overview 41 - Discrete Mathematics

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8 questions

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6 sample questions

Question 1.
Define what is meant by the order of a finite field.
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Think about how many elements there can be.
Question 2.
What is the characteristic of a finite field?
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Recall the prime numbers we discussed in class.
3Question 3.
What is the order of a finite field with characteristic 5 and r=3?
- 15
- 125
- 5
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Apply the formula we've discussed when calculating.
4Question 4.
True or False: The characteristic of a finite field can be a composite number.
- True
- False
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Recall our definition of characteristic.
Question 5.
Given a finite field of order 16, derive its characteristic and explain how this characteristic affects operations within the field.
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Consider how powers of primes work in defining order.
Question 6.
Using the irreducible polynomial x^2 + x + 1, construct a finite field and show all elements.
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Use a systematic approach to list all possible combinations.

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