Practice Carmichael Numbers and Pseudoprimes - 12.4 | 12. Introduction to Fermat’s Little Theorem and Primality Testing | Discrete Mathematics - Vol 3
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Carmichael Numbers and Pseudoprimes

12.4 - Carmichael Numbers and Pseudoprimes

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.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does Fermat's Little Theorem state?

💡 Hint: Think about the relationship between primes and modular arithmetic.

Question 2 Easy

Give an example of a composite pseudoprime.

💡 Hint: Recall the specific instance we discussed in class.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Fermat's Little Theorem establish?

It proves that all composite numbers satisfy a^(n-1) ≡ 1.
If p is prime
then a^(p-1) ≡ 1 (mod p).
It applies only to even numbers.

💡 Hint: Think about the relationship between prime numbers and modular arithmetic.

Question 2

Carmichael numbers are:

True
False

💡 Hint: What is the definition of a Carmichael number?

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Cryptographic algorithms often use Fermat’s theorem for primality testing. Design a potential algorithm that addresses both pseudoprimes and Carmichael numbers.

💡 Hint: Consider various bases instead of just one.

Challenge 2 Hard

Given a list of numbers, identify possible pseudoprimes and Carmichael numbers.

💡 Hint: A pseudoprime meets the conditions for selective bases; Carmichael for all—distinguish between them!

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.