Practice Definition Of Pseudoprimes (12.4.1) - Introduction to Fermat’s Little Theorem and Primality Testing

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6 sample questions

Question 1.
Define what a pseudoprime is.
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Think about the related concept of primality testing.
Question 2.
Give an example of a Carmichael number.
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Recall that it satisfies specific conditions for all coprime bases.
3Question 3.
What defines a pseudoprime?
- A prime number
- A composite number satisfying Fermat's Theorem
- A number that is always prime
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Focus on its relation to Fermat’s theorem.
4Question 4.
True or False: All Carmichael numbers are pseudoprime.
- True
- False
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Recall the definitions of both concepts.
Question 5.
Prove that a number which is not a pseudoprime cannot pass primality tests for every base.
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Consider analyzing the conditions laid out by Fermat's theorem as you reason through.
Question 6.
Given a composite number, demonstrate how to identify if it is a Carmichael number.
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Use the definition of Carmichael numbers to guide your reasoning.

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