Practice Carmichael Numbers - 12.1.7 | 12. Introduction to Fermat’s Little Theorem and Primality Testing | Discrete Mathematics - Vol 3
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Carmichael Numbers

12.1.7 - Carmichael Numbers

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

State Fermat's Little Theorem.

💡 Hint: Focus on the exponent and the condition of divisibility.

Question 2 Easy

Is 561 a prime number?

💡 Hint: Think about factorization.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Fermat's Little Theorem state?

If p is prime and a is any integer
then a^(p-1) ≡ 1 (mod p)
If n is composite and a is a prime number
then a^n ≡ 0 (mod n)
If p is prime and a is divisible by p
then a^(p-1) ≠ 1 (mod p)

💡 Hint: Focus on the role of prime numbers and congruences.

Question 2

Carmichael numbers are:

True
False

💡 Hint: Consider their relationship to primality testing.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Find another example of a Carmichael number and prove it using Fermat's theorem.

💡 Hint: Factor the Carmichael number to find key primes.

Challenge 2 Hard

Discuss how knowledge of Carmichael numbers can improve cryptographic algorithms.

💡 Hint: Think about how false positives could compromise security.

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Reference links

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