**Definition**: Even and Odd Numbers

An integer $n$ is called **even**, if it is divisible by $2$ (i.e. $2\mid n$), otherwise (i.e. if $2\not\mid n$) it is called **odd.**

### Examples

- $0,2,10,-20,250,\ldots$ are even.
- $1,-1,3,-3,255,-33,\ldots$ are odd.

| | | | | created: 2019-03-31 00:26:06 | modified: 2019-05-12 08:47:26 | by: *bookofproofs* | references: [1272]

## 1.**Proposition**: Every Integer Is Either Even or Odd

## 2.**Proposition**: Product of Two Even Numbers

## 3.**Proposition**: Product of Two Odd Numbers

## 4.**Proposition**: Product of an Even and an Odd Number

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[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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