Practice Applications in Primality Testing - 12.3 | 12. Introduction to Fermat’s Little Theorem and Primality Testing | Discrete Mathematics - Vol 3
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Applications in Primality Testing

12.3 - Applications in Primality Testing

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

State Fermat's Little Theorem.

💡 Hint: Think about what prime means.

Question 2 Easy

What is a pseudo prime?

💡 Hint: It behaves like a prime for certain tests.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Fermat's Little Theorem state?

A number raised to its modulus is always 1.
If p is prime
then a^(p-1) ≡ 1 (mod p) for a not divisible by p.
Only even numbers are prime.

💡 Hint: Focus on primes and powers.

Question 2

True or False: Carmichael numbers are primes.

True
False

💡 Hint: Think about what defines a prime number.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Determine the number of distinct Carmichael numbers up to 1000, utilizing the properties discussed in class.

💡 Hint: Check the composite nature and co-prime conditions.

Challenge 2 Hard

If we observe that b^(n-1) ≡ 1 (mod n) for various bases, how can we design a further verification step using another theorem or method?

💡 Hint: Think of double-checking solutions through additional methodologies.

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Reference links

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