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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State Fermat's Little Theorem in your own words.
💡 Hint: Think about what happens when you raise numbers that fit this requirement.
Question 2
Easy
What is a Carmichael number? Give an example.
💡 Hint: These numbers can fool primality tests!
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
Which statement accurately describes Fermat's Little Theorem?
- If p is prime and a is any integer
- then a^(p-1) ≡ 0 (mod p)
- If p is prime and a is co-prime to p
- then a^(p-1) ≡ 1 (mod p)
- Carmichael numbers are prime
💡 Hint: Which option keeps the focus on co-primality?
Question 2
True or False: All composite numbers are Carmichael numbers.
- True
- False
💡 Hint: Think about examples of composites that are not Carmichael.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the number 561, demonstrate why it is a Carmichael number using Fermat’s Little Theorem for bases 2, 3, and 5.
💡 Hint: Use Fermat's theorem for your calculations.
Question 2
Construct your primality testing algorithm incorporating Fermat’s theorem, listing steps you would take to strengthen it against Carmichael numbers.
💡 Hint: Think about involving multiple tests!
Challenge and get performance evaluation