Definition:Even Integer/Definition 3

Definition

An integer $n \in \Z$ is even if and only if:

$x \equiv 0 \pmod 2$

where the notation denotes congruence modulo $2$.

Also see

• Equivalence of Definitions of Even Integer

• Definition:Odd Integer

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 $\text A.3$
• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $2$: Maps and relations on sets: Example $2.23$