# Definition:Odd Integer/Odd-Times Odd

< Definition:Odd Integer(Redirected from Definition:Odd-Times Odd Integer)

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## Contents

## Definition

Let $n \in \Z$, i.e. let $n$ be an integer.

### Definition 1

$n$ is **odd-times odd** if and only if it is an odd number greater than $1$ which is not prime.

### Definition 2

$n$ is **odd-times odd** if and only if there exist odd numbers $x, y > 1$ such that $n = x y$.

### Sequence

The sequence of **odd-times odd integers** begins:

- $9, 15, 21, 25, 27, \ldots$

## Euclid's Definition

In the words of Euclid:

*An***odd-times odd number**is that which is measured by an odd number according to an odd number.

(*The Elements*: Book $\text{VII}$: Definition $10$)