Practice Introduction to Fermat’s Little Theorem and Primality Testing - 12.1.1 | 12. Introduction to Fermat’s Little Theorem and Primality Testing | Discrete Mathematics - Vol 3
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Introduction to Fermat’s Little Theorem and Primality Testing

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

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is Fermat's Little Theorem?

💡 Hint: Focus on the relationship between primes and coprime integers.

Question 2 Easy

Give an example of two coprime numbers.

💡 Hint: Check their prime factors to see if they share any.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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.

💡 Hint: Think of relationships between primes and their determinants.

Question 2

True or False: Carmichael numbers can pass Fermat's test for any base.

True
False

💡 Hint: Recall definitions of Carmichael numbers and their properties.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that there exist composite numbers that are Carmichael numbers. Give an example.

💡 Hint: Investigate how the prime factorization relates to Fermat’s conditions.

Challenge 2 Hard

If you have an arbitrary integer n that is not prime, suggest a primality test using Fermat's theorem.

💡 Hint: Identify bases that offer the best logical coverage in the integer space.

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