12.1.8. Conclusion

Try these first

1. 1.

   State Fermat's Little Theorem.

   Hint

   Think about the prime number and its co-primality with 'a'.

2. 2.

   What are Carmichael numbers?

   Hint

   Recall the relationship between composites and primes.

3. 3.

   What does Fermat's Little Theorem state?

   • It applies to even numbers only.
   • It applies to odd numbers only.
   • It applies to prime numbers.

   Hint

   Remember the conditions around primes in mathematics.

4. 4.

   Is the number 561 prime?

   • True
   • False

   Hint

   Recall the characteristics unique to prime versus composite numbers.

5. 5.

   Prove that 561 is a Carmichael number.

   Hint

   No hint provided

6. 6.

   Apply Fermat's theorem to validate a large number, say 101 with base 5.

   Hint

   Remember the methodology examining the base in our previous classes.