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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does Fermat's Little Theorem state for prime p?
💡 Hint: Think about the relationship between primes and modular arithmetic.
Question 2
Easy
Provide an example of a Carmichael number.
💡 Hint: Carmichael numbers are always composite.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
According to Fermat's Little Theorem, if p is prime and a is coprime to p, what is true?
- `a^p ≡ 0 mod p`
- `a^(p-1) ≡ 1 mod p`
- `p^a ≡ a mod p`
💡 Hint: Recall the main statement of the theorem.
Question 2
Are Carmichael numbers always prime?
- True
- False
💡 Hint: Think of their definition and characteristics.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that 341 is a Carmichael number using Fermat's test for a random base.
💡 Hint: Pick bases carefully that are less than `341`.
Question 2
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!
Challenge and get performance evaluation