even number

Definition Suppose k is an integer. If there exists an integer r such that k=2r+1, then k is an odd numberMathworldPlanetmathPlanetmath. If there exists an integer r such that k=2r, then k is an even number.

The concept of even and odd numbers are most easily understood in the binary base. Then the above definition simply that even numbers end with a 0, and odd numbers end with a 1.

0.0.1 Properties

  1. 1.

    Every integer is either even or . This can be proven using induction, or using the fundamental theorem of arithmeticMathworldPlanetmath.

  2. 2.

    An integer k is even () if and only if k2 is even ().

Title even number
Canonical name EvenNumber
Date of creation 2013-03-22 13:56:29
Last modified on 2013-03-22 13:56:29
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 10
Author mathcam (2727)
Entry type Definition
Classification msc 11-00
Classification msc 03-00
Related topic NumberOdd
Defines odd number
Defines even integer
Defines odd integer
Defines even
Defines odd