12.2.1. Statement and Explanation

Try these first

1. 1.

   State Fermat's Little Theorem.

   Hint

   It speaks about primes and their co-primes.

2. 2.

   What does it mean for two numbers to be co-prime?

   Hint

   Think of common factors.

3. 3.

   What is a requirement of Fermat's Little Theorem?

   • p must be odd
   • p must be prime
   • a must be even
   • a must be odd

   Hint

   Look at the definition of primes.

4. 4.

   True or False? Carmichael numbers are prime numbers.

   • True
   • False

   Hint

   Recall the definition of Carmichael numbers.

5. 5.

   Using Fermat's theorem, verify if 19 is prime by applying the theorem with bases 2, 3, and 4.

   Hint

   Use Fermat's theorem conditions.

6. 6.

   Can you prove or disprove that 49 is composite using primality testing?

   Hint

   Remember properties of non-primes.