Practice Carmichael Numbers And Pseudoprimes (12.4) - Introduction to Fermat’s Little Theorem and Primality Testing

Practice: Carmichael Numbers and Pseudoprimes

Lesson 12.4Introduction to Fermat’s Little Theorem and Primality Testing

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8 questions

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6 sample questions

Question 1.
What does Fermat's Little Theorem state?
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Think about the relationship between primes and modular arithmetic.
Question 2.
Give an example of a composite pseudoprime.
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Recall the specific instance we discussed in class.
3Question 3.
What does Fermat's Little Theorem establish?
- It proves that all composite numbers satisfy a^(n-1) ≡ 1.
- If p is prime
- then a^(p-1) ≡ 1 (mod p).
- It applies only to even numbers.
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Think about the relationship between prime numbers and modular arithmetic.
4Question 4.
Carmichael numbers are:
- True
- False
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What is the definition of a Carmichael number?
Question 5.
Cryptographic algorithms often use Fermat’s theorem for primality testing. Design a potential algorithm that addresses both pseudoprimes and Carmichael numbers.
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Consider various bases instead of just one.
Question 6.
Given a list of numbers, identify possible pseudoprimes and Carmichael numbers.
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A pseudoprime meets the conditions for selective bases; Carmichael for all—distinguish between them!

4 more questions in this section. Enroll free to practise them all.