12.3.1. Using Fermat's Little Theorem for Modular Arithmetic

Try these first

1. 1.

   What does Fermat's Little Theorem state?

   Hint

   Think about the relationship involving prime numbers.

2. 2.

   Provide an example of a pseudoprime.

   Hint

   Consider numbers that pass the Fermat test but are not prime.

3. 3.

   What does Fermat's Little Theorem state?

   Hint

   Focus on the relationship between primes and modular arithmetic.

4. 4.

   True or False: Every pseudoprime is a prime number.

   • True
   • False

   Hint

   Recall the definition of pseudoprimes.

5. 5.

   Prove that the number 341 is a pseudoprime to base 2 by demonstrating that 2^340 ≡ 1 (mod 341).

   Hint

   Simplify your calculation using smaller powers and modular arithmetic.

6. 6.

   Create a composite number larger than 100 that is also a Carmichael number. Verify that it satisfies the conditions.

   Hint

   Look for composite numbers that are products of distinct primes.