ABSTRACT
This chapter discusses the foundations of number theory. It begins with the concept of divisibility. As author shall see there is a subset of the integers that will allow us to write all integers as products of them. These numbers are the prime numbers and they are the building blocks of the integers. Much of what they discuss in this chapter is covered in the number theory books of Euclid’s Elements. One of these results is the concept of greatest common divisor which is defined multiplicatively, but, because of Euclid’s Algorithm, can be found through a process than in essence involves only addition and subtraction. With these results in hand they can then prove that integers can be uniquely factored into prime numbers.
