Practice Proof Overview (12.2.2) - Introduction to Fermat’s Little Theorem and Primality Testing

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6 sample questions

Question 1.
What does Fermat's Little Theorem state?
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Think about how integers behave under prime moduli.
Question 2.
Is 341 a Carmichael number?
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Review the characteristics of Carmichael numbers.
3Question 3.
What does Fermat's Little Theorem relate to?
- Determining roots
- Arithmetic under primes
- Finding patterns
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Focus on how it connects integers and primes.
4Question 4.
True or False: Carmichael numbers are always prime.
- True
- False
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Think about the characteristics of these numbers.
Question 5.
How many distinct integers a exist for a prime p such that a < p and GCD(a, p) = 1?
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Consider the properties of prime numbers.
Question 6.
If a number n is found to be a Carmichael number, what does this imply for any potential primality tests?
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Review the definitions of pseudo primes in relation to Fermat's theorem.

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