Practice Introduction To Fermat’s Little Theorem And Primality Testing (12.1.1)

Practice: Introduction to Fermat’s Little Theorem and Primality Testing

Lesson 12.1.1Introduction to Fermat’s Little Theorem and Primality Testing

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9 questions

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6 sample questions

Question 1.
What is Fermat's Little Theorem?
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Focus on the relationship between primes and coprime integers.
Question 2.
Give an example of two coprime numbers.
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Check their prime factors to see if they share any.
3Question 3.
What does Fermat's Little Theorem state?
- a) It applies only to even numbers.
- b) If p is prime
- a^(p-1) ≡ 1 (mod p) for coprime a.
- c) All composite numbers are prime.
- d) Only prime squares satisfy it.
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Think of relationships between primes and their determinants.
4Question 4.
True or False: Carmichael numbers can pass Fermat's test for any base.
- True
- False
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Recall definitions of Carmichael numbers and their properties.
Question 5.
Prove that there exist composite numbers that are Carmichael numbers. Give an example.
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Investigate how the prime factorization relates to Fermat’s conditions.
Question 6.
If you have an arbitrary integer n that is not prime, suggest a primality test using Fermat's theorem.
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Identify bases that offer the best logical coverage in the integer space.

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