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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: Recall the conditions regarding p and a.
Question 2
Easy
What does it mean for two numbers to be co-prime?
💡 Hint: Think about the factors of the numbers.
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?
- a^(p-1) ≡ 0 (mod p)
- a^(p-1) ≡ 1 (mod p)
- a^(p) ≡ 1 (mod p)
💡 Hint: Think about the prime’s relation with its multiples.
Question 2
Carmichael numbers behave like primes under which condition?
- True
- False
💡 Hint: Recall the definition of Carmichael numbers.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a prime p = 17, find an integer a that satisfies Fermat's Little Theorem, and prove it.
💡 Hint: Reduce 10^(16) step by step modulo 17.
Question 2
For the Carmichael number 561, show all bases up to 10 satisfy Fermat's Little Theorem.
💡 Hint: Recall the properties of modular arithmetic.
Challenge and get performance evaluation