Practice Proof By Contradiction (22.3.2.1) - Finite Fields and Properties I

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6 sample questions

Question 1.
What does the characteristic of a field represent?
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Think about addition and returning to zero.
Question 2.
Define what a prime number is.
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Consider how many factors it has.
3Question 3.
What denotes the characteristic of a field?
- The sum of all elements
- The additive order of multiplicative identity
- The highest number in the field
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Think of how elements interact in addition.
4Question 4.
True or False: The characteristic of any finite field must be a prime number.
- True
- False
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Recall the definitions and the implications of composite numbers.
Question 5.
Find the characteristic of the finite field containing the elements {0, 1, 2} with operations defined by addition and multiplication modulo 3.
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Focus on how the operations cycle through the elements.
Question 6.
If we assume a field has a characteristic of 6, demonstrate how you would derive a contradiction.
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Break the assumption into cases for each factor of 6.

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