12.1.3. Corollary of Fermat's Little Theorem

Try these first

1. 1.

   What does Fermat's Little Theorem state?

   Hint

   Think about the relationship between primes and coprime integers.

2. 2.

   Define Carmichael numbers.

   Hint

   They trick primality tests!

3. 3.

   What does Fermat's Little Theorem establish?

   • Prime relationship with multiplication
   • Behavior of powers under modular arithmetic
   • Divisibility rules

   Hint

   Recall the theorem's specifics.

4. 4.

   Are Carmichael numbers prime numbers?

   • True
   • False

   Hint

   Think about their characteristics.

5. 5.

   Determine if 561 is prime using Fermat's theorem with b = 2.

   Hint

   Use the properties of modular arithmetic.

6. 6.

   Prove that for any prime p, it holds that (p-1)! ≡ -1 (mod p).

   Hint

   Consider the properties of factorials and how they relate to primes.