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

which is divisible by 2 and hence is even.

See also

Connell Sequence, Doubly Even Number, Even Function, Odd Number, Parity, Singly Even Number

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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 Number

Cite this as:

Weisstein, Eric W. "Even Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EvenNumber.html

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