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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: Think about how it relates to primes and modular arithmetic.
Question 2
Easy
Explain what a pseudo prime is.
💡 Hint: Consider an example of a composite number.
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 for a prime p?
- a^(p-1) ≡ 1 (mod p)
- a^(p) ≡ 1 (mod p)
- p | a
- gcd(a
- p) = 0
💡 Hint: Recall the theorem definition directly.
Question 2
Is 341 a pseudo prime?
- True
- False
💡 Hint: Think about its factors.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that 561 is a Carmichael number by demonstrating it satisfies Fermat's theorem for all valid bases.
💡 Hint: Tackle it by considering GCD conditions for 3, 11, and 17, and apply Fermat's theorem.
Question 2
Find a composite number greater than 100 which is not a Carmichael number and explain why it fails the Fermat test.
💡 Hint: Test various bases and demonstrate a failure in at least one case.
Challenge and get performance evaluation