An even number is an integer of the form 
,
where 
is an integer.
The even numbers are therefore ..., 
, 
,
0, 2, 4, 6, 8, 10, ... (with the nonnegative portion given by 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 positive even numbers, for 
,
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)],](/images/equations/EvenNumber/NumberedEquation2.svg) |
which is divisible by 2 and hence is even.
