12.1.2. Fermat's Little Theorem

Try these first

1. 1.

   What does Fermat's Little Theorem state?

   Hint

   Think of how powers relate to prime numbers.

2. 2.

   What is a prime number?

   Hint

   Consider the smallest prime numbers.

3. 3.

   What does Fermat's Little Theorem relate to?

   • Prime Numbers
   • Even Numbers
   • Odd Numbers

   Hint

   Understand the context of prime numbers.

4. 4.

   If p = 11 and a = 10, what is a^(p-1) mod p?

   Hint

   Calculate using Fermat's theorem!

5. 5.

   Using Fermat's theorem, prove that for any number a co-prime to p, a^(p-1) mod p indeed equals 1 through an example.

   Hint

   Focus on the computation of powers in modulo.

6. 6.

   Explain the significance of Carmichael numbers in the context of Fermat's theorem.

   Hint

   Reflect on how they relate to both Fermat's theorem and composite numbers.