12.1.1 - Introduction to Fermat’s Little Theorem and Primality Testing
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Practice Questions
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What is Fermat's Little Theorem?
💡 Hint: Focus on the relationship between primes and coprime integers.
Give an example of two coprime numbers.
💡 Hint: Check their prime factors to see if they share any.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Fermat's Little Theorem state?
💡 Hint: Think of relationships between primes and their determinants.
True or False: Carmichael numbers can pass Fermat's test for any base.
💡 Hint: Recall definitions of Carmichael numbers and their properties.
1 more question available
Challenge Problems
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Prove that there exist composite numbers that are Carmichael numbers. Give an example.
💡 Hint: Investigate how the prime factorization relates to Fermat’s conditions.
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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