In this and the subsequent problems, you will be working in a different number system. The goal is to illustrate that unique factorization of prime numbers is a special feature of the integers. We...

In this and the subsequent problems, you will be working in a different number system. The goal is to illustrate that unique factorization of prime numbers is a special feature of the integers.

We consider all numbers of the form

where a and b are integers. For example
 3 is a number in this system,
 2 is not. This number system is denoted
  is the set

Please do the following: