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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?
💡 Hint: Think about the relationship between primes and modular arithmetic.
Question 2
Easy
Give an example of a composite pseudoprime.
💡 Hint: Recall the specific instance we discussed in class.
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
What does Fermat's Little Theorem establish?
- It proves that all composite numbers satisfy a^(n-1) ≡ 1.
- If p is prime
- then a^(p-1) ≡ 1 (mod p).
- It applies only to even numbers.
💡 Hint: Think about the relationship between prime numbers and modular arithmetic.
Question 2
Carmichael numbers are:
- True
- False
💡 Hint: What is the definition of a Carmichael number?
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Cryptographic algorithms often use Fermat’s theorem for primality testing. Design a potential algorithm that addresses both pseudoprimes and Carmichael numbers.
💡 Hint: Consider various bases instead of just one.
Question 2
Given a list of numbers, identify possible pseudoprimes and Carmichael numbers.
💡 Hint: A pseudoprime meets the conditions for selective bases; Carmichael for all—distinguish between them!
Challenge and get performance evaluation