Even Number

An Integer of the form $N=2n$, where $n$ is an Integer. The even numbers are therefore ..., $-4$, $-2$, 0, 2, 4, 6, 8, 10, ... (Sloane's A005843). Since the even numbers are integrally divisible by two, $N\equiv 0\ \left({{\rm mod\ } {2}}\right)$ for even $N$. An even number $N$ for which $N\equiv 2\ \left({{\rm mod\ } {4}}\right)$ is called a Singly Even Number, and an even number $N$ for which $N\equiv 0\ \left({{\rm mod\ } {4}}\right)$ is called a Doubly Even Number. An integer which is not even is called an Odd Number. The Generating Function of the even numbers is

$${2x\over(x-1)^2}=2x+4x^2+6x^3+8x^4+\ldots.$$

See also Doubly Even Number, Even Function, Odd Number, Singly Even Number

References

Sloane, N. J. A. Sequence A005843/M0985 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.