Practice Primality Testing Algorithms (12.1.6) - 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 for prime p?
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Think about the relationship between primes and modular arithmetic.
Question 2.
Provide an example of a Carmichael number.
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Carmichael numbers are always composite.
3Question 3.
According to Fermat's Little Theorem, if p is prime and a is coprime to p, what is true?
- `a^p ≡ 0 mod p`
- `a^(p-1) ≡ 1 mod p`
- `p^a ≡ a mod p`
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Recall the main statement of the theorem.
4Question 4.
Are Carmichael numbers always prime?
- True
- False
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Think of their definition and characteristics.
Question 5.
Prove that 341 is a Carmichael number using Fermat's test for a random base.
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Pick bases carefully that are less than `341`.
Question 6.
Create a detailed algorithm that efficiently uses Fermat's theorem to compute a^b mod p, explaining each step.
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Think about employing the divide-and-conquer strategy!

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