# even number

Definition Suppose $k$ is an integer. If there exists an integer $r$ such that $k=2r+1$, then $k$ is an . 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. 1.

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

2. 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