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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
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.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that there exist composite numbers that are Carmichael numbers. Give an example.
💡 Hint: Investigate how the prime factorization relates to Fermat’s conditions.
Question 2
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.
Challenge and get performance evaluation