12.1.6 - Primality Testing Algorithms
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Practice Questions
Test your understanding with targeted questions
What does Fermat's Little Theorem state for prime p?
💡 Hint: Think about the relationship between primes and modular arithmetic.
Provide an example of a Carmichael number.
💡 Hint: Carmichael numbers are always composite.
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Interactive Quizzes
Quick quizzes to reinforce your learning
According to Fermat's Little Theorem, if p is prime and a is coprime to p, what is true?
💡 Hint: Recall the main statement of the theorem.
Are Carmichael numbers always prime?
💡 Hint: Think of their definition and characteristics.
1 more question available
Challenge Problems
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Prove that 341 is a Carmichael number using Fermat's test for a random base.
💡 Hint: Pick bases carefully that are less than `341`.
Create a detailed algorithm that efficiently uses Fermat's theorem to compute a^b mod p, explaining each step.
💡 Hint: Think about employing the divide-and-conquer strategy!
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