even number
Definition Suppose $k$ is an integer. If there exists an integer $r$ such that $k=2r+1$, then $k$ is an odd number^{}. If there exists an integer $r$ such that $k=2r$, then $k$ is an even number.
The concept of even and odd numbers are most easily understood in the binary base. Then the above definition simply that even numbers end with a $0$, and odd numbers end with a $1$.
0.0.1 Properties

1.
Every integer is either even or . This can be proven using induction, or using the fundamental theorem of arithmetic^{}.

2.
An integer $k$ is even () if and only if ${k}^{2}$ is even ().
Title  even number 
Canonical name  EvenNumber 
Date of creation  20130322 13:56:29 
Last modified on  20130322 13:56:29 
Owner  mathcam (2727) 
Last modified by  mathcam (2727) 
Numerical id  10 
Author  mathcam (2727) 
Entry type  Definition 
Classification  msc 1100 
Classification  msc 0300 
Related topic  NumberOdd 
Defines  odd number 
Defines  even integer 
Defines  odd integer 
Defines  even 
Defines  odd 