Definition:Even Integer/Definition 1

Definition

An integer $n \in \Z$ is even if and only if it is divisible by $2$.

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

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $24$. The Division Algorithm
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): even