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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State Fermat's Little Theorem.
💡 Hint: Focus on the exponent and the condition of divisibility.
Question 2
Easy
Is 561 a prime number?
💡 Hint: Think about factorization.
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 state?
- If p is prime and a is any integer
- then a^(p-1) ≡ 1 (mod p)
- If n is composite and a is a prime number
- then a^n ≡ 0 (mod n)
- If p is prime and a is divisible by p
- then a^(p-1) ≠ 1 (mod p)
💡 Hint: Focus on the role of prime numbers and congruences.
Question 2
Carmichael numbers are:
- True
- False
💡 Hint: Consider their relationship to primality testing.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find another example of a Carmichael number and prove it using Fermat's theorem.
💡 Hint: Factor the Carmichael number to find key primes.
Question 2
Discuss how knowledge of Carmichael numbers can improve cryptographic algorithms.
💡 Hint: Think about how false positives could compromise security.
Challenge and get performance evaluation