Number Theory

Elementary number theory is the study of the relationships among the integers. These relationships arise from two properties:

(1) Under the operations of addition and multiplication, the integers form an integral domain - both operations are commutative and associative, there is an additive identity 0 and a multiplicative identity 1, every integer has an additive inverse, multiplication is distributive over addition, and the product of two non-zero numbers can't be zero.

(2) More importantly, the set of positive integers is wellordered; that is, every non-empty subset of positive integers has an integer in it which is smaller than any of the other integers in that subset.