12.3.2 - Primality Testing Algorithm Limitations
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Practice Questions
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What is Fermat's Little Theorem?
💡 Hint: Think about how it relates to primes and modular arithmetic.
Explain what a pseudo prime is.
💡 Hint: Consider an example of a composite number.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Fermat's Little Theorem state for a prime p?
💡 Hint: Recall the theorem definition directly.
Is 341 a pseudo prime?
💡 Hint: Think about its factors.
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Challenge Problems
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Prove that 561 is a Carmichael number by demonstrating it satisfies Fermat's theorem for all valid bases.
💡 Hint: Tackle it by considering GCD conditions for 3, 11, and 17, and apply Fermat's theorem.
Find a composite number greater than 100 which is not a Carmichael number and explain why it fails the Fermat test.
💡 Hint: Test various bases and demonstrate a failure in at least one case.
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