# Definition:Even Integer/Definition 2

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## Definition

An integer $n \in \Z$ is **even** if and only if it is of the form:

- $n = 2 r$

where $r \in \Z$ is an integer.

## Also see

- Results about
**even integers**can be found**here**.

## Historical Note

The concept of classifying numbers as **odd** or **even** appears to have originated with the Pythagoreans.

It was their belief that **even numbers** are **female**, and **odd numbers** are **male**.

A commentator on Plato used the term **isosceles number** for an **even number**, in correspondence with the concept of an isosceles triangle. In a similar way an odd number was described as **scalene**.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): Appendix $\text{A}.5$: Theorems and Proofs: Example $\text A.3$ - 1980: David M. Burton:
*Elementary Number Theory*(revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.1$ The Division Algorithm - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.2$: More about Numbers: Irrationals, Perfect Numbers and Mersenne Primes