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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State Fermat's Little Theorem.
💡 Hint: Think about the relation between primes and modular arithmetic.
Question 2
Easy
What is an example of a Carmichael number?
💡 Hint: Recall that it misleads primality tests while being composite.
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?
- If p is prime
- then a^p ≡ 0 (mod p)
- If p is prime
- then a^(p-1) ≡ 1 (mod p)
- If a is even
- a^2 is even
💡 Hint: Remember the key formula in the theorem.
Question 2
Is 561 a prime number?
- True
- False
💡 Hint: Recollect the definition of prime numbers.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if a number n satisfies b^(n-1) ≡ 1 for all bases b co-prime to n, then n is a Carmichael number.
💡 Hint: Use the prime factorization of n and analyze the implications for all bases.
Question 2
In a practical application, explain how one could modify a basic primality test to take Carmichael numbers into account.
💡 Hint: Consider the diversity of bases used in testing.
Challenge and get performance evaluation