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# 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 states 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 odd. This can be proven using induction, or using the fundamental theorem of arithmetic.

2. An integer $k$ is even (odd) if and only if $k^{2}$ is even (odd).

Defines:

odd number, even integer, odd integer, even, odd

Related:

NumberOdd

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11-00*no label found*03-00

*no label found*

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