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	2013-03-22 13:56:29
Last modified on	2013-03-22 13:56:29
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	10
Author	mathcam (2727)
Entry type	Definition
Classification	msc 11-00
Classification	msc 03-00
Related topic	NumberOdd
Defines	odd number
Defines	even integer
Defines	odd integer
Defines	even
Defines	odd