Definition:Even Integer/Even-Times Even

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

• Definition:Even Integer
• Definition:Even-Times Odd Integer

• Definition:Odd Integer

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): $4$