Practice Applications In Primality Testing (12.3) - Introduction to Fermat’s Little Theorem and Primality Testing

Practice: Applications in Primality Testing

Lesson 12.3Introduction to Fermat’s Little Theorem and Primality Testing

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
State Fermat's Little Theorem.
Show hintHide hint
Think about what prime means.
Question 2.
What is a pseudo prime?
Show hintHide hint
It behaves like a prime for certain tests.
3Question 3.
What does Fermat's Little Theorem state?
- A number raised to its modulus is always 1.
- If p is prime
- then a^(p-1) ≡ 1 (mod p) for a not divisible by p.
- Only even numbers are prime.
Show hintHide hint
Focus on primes and powers.
4Question 4.
True or False: Carmichael numbers are primes.
- True
- False
Show hintHide hint
Think about what defines a prime number.
Question 5.
Determine the number of distinct Carmichael numbers up to 1000, utilizing the properties discussed in class.
Show hintHide hint
Check the composite nature and co-prime conditions.
Question 6.
If we observe that b^(n-1) ≡ 1 (mod n) for various bases, how can we design a further verification step using another theorem or method?
Show hintHide hint
Think of double-checking solutions through additional methodologies.

4 more questions in this section. Enroll free to practise them all.