12.3.1 - Using Fermat's Little Theorem for Modular Arithmetic
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Practice Questions
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What does Fermat's Little Theorem state?
💡 Hint: Think about the relationship involving prime numbers.
Provide an example of a pseudoprime.
💡 Hint: Consider numbers that pass the Fermat test but are not prime.
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Interactive Quizzes
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What does Fermat's Little Theorem state?
💡 Hint: Focus on the relationship between primes and modular arithmetic.
True or False: Every pseudoprime is a prime number.
💡 Hint: Recall the definition of pseudoprimes.
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Challenge Problems
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Prove that the number 341 is a pseudoprime to base 2 by demonstrating that 2^340 ≡ 1 (mod 341).
💡 Hint: Simplify your calculation using smaller powers and modular arithmetic.
Create a composite number larger than 100 that is also a Carmichael number. Verify that it satisfies the conditions.
💡 Hint: Look for composite numbers that are products of distinct primes.
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