Practice Applications of Fermat's Little Theorem - 12.1.5 | 12. Introduction to Fermat’s Little Theorem and Primality Testing | Discrete Mathematics - Vol 3
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Applications of Fermat's Little Theorem

12.1.5 - Applications of Fermat's Little Theorem

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does Fermat's Little Theorem state?

💡 Hint: Focus on the conditions involving **p** and **a**.

Question 2 Easy

Give an example of a number that is co-prime to 7.

💡 Hint: Think about multiples.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Fermat's Little Theorem allow us to conclude if b^(p-1) ≡ 1 (mod p)?

**p is prime**
**p is composite**
**a is prime**

💡 Hint: Remember valid conditions of the theorem.

Question 2

Is the statement 'All Carmichael numbers are prime' true?

True
False

💡 Hint: Recall the definition of a Carmichael number.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using Fermat's Little Theorem, prove that a^(p-1) ≡ 1 (mod p) holds for large p and any a co-prime to it. Provide an example.

💡 Hint: Select a prime larger than 10.

Challenge 2 Hard

Explore the implications of Carmichael numbers. Investigate if any Carmichael numbers exist and discuss their significance.

💡 Hint: Use online mathematical databases or number theory resources.

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