# Definition:Even Integer/Even-Times Even

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## Definition

Let $n$ be an integer.

Then $n$ is **even-times even** if and only if it has $4$ as a divisor.

The first few non-negative **even-times even** numbers are:

- $0, 4, 8, 12, 16, 20, \ldots$

This sequence is A008586 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Euclid's Definition

In the words of Euclid:

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

(*The Elements*: Book $\text{VII}$: Definition $8$)

## Also known as

An **even-times even integer** can also be referred to as an **even-even integer**.

## Also see

## Historical Note

The introduction of the category of **even-times even integers** originated with the Pythagoreans.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $4$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $4$