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