Practice Final Remarks on Number Theory - 12.5.2 | 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

Final Remarks on Number Theory

12.5.2 - Final Remarks on Number Theory

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

State Fermat's Little Theorem in your own words.

💡 Hint: Think about what happens when you raise numbers that fit this requirement.

Question 2 Easy

What is a Carmichael number? Give an example.

💡 Hint: These numbers can fool primality tests!

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which statement accurately describes Fermat's Little Theorem?

If p is prime and a is any integer
then a^(p-1) ≡ 0 (mod p)
If p is prime and a is co-prime to p
then a^(p-1) ≡ 1 (mod p)
Carmichael numbers are prime

💡 Hint: Which option keeps the focus on co-primality?

Question 2

True or False: All composite numbers are Carmichael numbers.

True
False

💡 Hint: Think about examples of composites that are not Carmichael.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the number 561, demonstrate why it is a Carmichael number using Fermat’s Little Theorem for bases 2, 3, and 5.

💡 Hint: Use Fermat's theorem for your calculations.

Challenge 2 Hard

Construct your primality testing algorithm incorporating Fermat’s theorem, listing steps you would take to strengthen it against Carmichael numbers.

💡 Hint: Think about involving multiple tests!

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.