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

• 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

• 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): $2$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): even number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): even number
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): even