Skip to content

Search AllRounder.ai

Search your courses, subjects, tracks, games and features, or jump straight to a page.

Enrol to start learning

Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.

Enrol free

12.2.2. Proof Overview

  • This section

    Practice test

    10 questions on this section. Wrong answers show you what to read again.

    Sign up to take it
  • Whole chapter

    Revision test

    Mixed questions from across the chapter. Your answers get marked.

    Sign up to take it
  • Quick

    Flashcard drill

    2 cards from this lesson. Good the night before a test.

Try these first

  1. 1.

    What does Fermat's Little Theorem state?

    Hint

    Think about how integers behave under prime moduli.

  2. 2.

    Is 341 a Carmichael number?

    Hint

    Review the characteristics of Carmichael numbers.

  3. 3.

    What does Fermat's Little Theorem relate to?

    • Determining roots
    • Arithmetic under primes
    • Finding patterns
    Hint

    Focus on how it connects integers and primes.

  4. 4.

    True or False: Carmichael numbers are always prime.

    • True
    • False
    Hint

    Think about the characteristics of these numbers.

  5. 5.

    How many distinct integers a exist for a prime p such that a < p and GCD(a, p) = 1?

    Hint

    Consider the properties of prime numbers.

  6. 6.

    If a number n is found to be a Carmichael number, what does this imply for any potential primality tests?

    Hint

    Review the definitions of pseudo primes in relation to Fermat's theorem.

Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

4 more questions available

Enrol free

Quiz

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

Get your answers marked and your progress tracked

Enrol free

Challenge Problems

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting