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Even Number
An even number is an integer of the form 
,
where 
is an integer.
The even numbers are therefore ..., 
, 
,
0, 2, 4, 6, 8, 10, ... (OEIS A005843). Since
the even numbers are integrally divisible by two, the congruence 
holds for even 
. An even number 
for which 
also holds is called a singly
even number, while an even number 
for which 
is called a doubly
even number. An integer which is not even is called an odd
number.
The oddness of a number is called its parity, so an odd number has parity 1, while an even number has parity 0.
The generating function of the even numbers is
 |
The product of an even number and an odd number is always even, as can be seen by writing
![(2k)(2l+1)=2[k(2l+1)],](https://mathworld.wolfram.com/images/equations/EvenNumber/NumberedEquation2.svg) |
which is divisible by 2 and hence is even.
See also
Connell Sequence, Doubly Even Number, Even Function, Odd Number, Parity, Singly Even NumberExplore with Wolfram|Alpha
References
Commission on Mathematics of the College Entrance Examination Board. Informal Deduction in Algebra: Properties of Odd and Even Numbers. Princeton, NJ, 1959.Sloane, N. J. A. Sequence A005843/M0985 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Even NumberCite this as:
Weisstein, Eric W. "Even Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EvenNumber.html