12.5.1 - Example of a Carmichael Number (561)
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
State Fermat's Little Theorem.
💡 Hint: Think about the relation between primes and modular arithmetic.
What is an example of a Carmichael number?
💡 Hint: Recall that it misleads primality tests while being composite.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does Fermat's Little Theorem state?
💡 Hint: Remember the key formula in the theorem.
Is 561 a prime number?
💡 Hint: Recollect the definition of prime numbers.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.