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
which is divisible by 2 and hence is even.
See also
Connell Sequence, Doubly Even Number, Even Function, Odd Number, Parity, Singly Even Number
Explore 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
Cite this as:
Weisstein, Eric W. "Even Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EvenNumber.html