Number Concepts, Prime Numbers, and the Division Algorithm

Abstract

Introduction The topic of this section is the divisibility of integers, the basic building blocks (called prime numbers) for integers, and how to apply this foundation to problem solving in combinatorics and word problems in which integers solutions are sought (Diophantine equations). Brief Description The operations of addition and multiplication are two ways to combine integers to get a third integer (this is called the closure property). We’ll now talk a bit about trying to do the operations in reverse (subtraction and division) and discuss the formal definitions which will give rise to the big question of this half of the text and the big theorem, Fundamental Theorem of Arithmetic, and its applications.