2. It is easy to show that the converse of Fermats Theorem does not hold; i.e., the congruence aⁿ = a (mod n) for all a does not imply that n is prime. A composite number n that satisfy this congruence is called a pseudoprime to base a.

1. Verify that 341 is a pseudoprime to base 2.
2. Verify that 91 is a pseudoprime to base 3.
3. Show that if p is prime and 2^p 1 iscomposite, then 2^p 1 is a pseudoprime to base 2.