write the general form of an even integer
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n=2k , k where is an integer and n is the integer
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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
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." FromMathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EvenNumber.html
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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
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." FromMathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EvenNumber.html
Wolfram Web ResourcesMathematica »
The #1 tool for creating Demonstrations and anything technical.
Wolfram|Alpha »
Explore anything with the first computational knowledge engine.
Wolfram Demonstrations Project »
Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.
Computerbasedmath.org »
Join the initiative for modernizing math education.
Online Integral Calculator »
Solve integrals with Wolfram|Alpha.
Step-by-step Solutions »
Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
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