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Difference between revisions of "Even integer"

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An '''even integer''' <math>n</math> is any [[integer]] which is a [[multiple]] of 2.  Every even integer can be written in the form <math>2k</math> for some unique integer <math>k</math>. The even integers with smallest [[absolute value]] are <math>0, 2, -2, 4, -4, \ldots</math>.  The sum and difference of any two even integers is even, and the product of any two even integers is not only even but is also [[divisible]] by 4. The sum of an even and an [[odd integer]] is odd.  Since every even integer is divisible by 2, 2 is the only [[prime]] even integer.
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An '''even integer''' is any [[integer]] which is a [[multiple]] of <math>2.</math>  The even integers are <math>\ldots, -4, -2, 0, 2, 4, \ldots</math>; specifically, note that <math>0</math> is even. Every even integer can be written in the form <math>2k</math> for some unique integer <math>k</math>.  
  
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The sum and difference of any two even integers is even, and the product of any two even integers is not only even but is also [[divisible]] by <math>4.</math>  The sum of an even integer and an [[odd integer]] is odd. 
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Since every even integer is divisible by <math>2,</math> <math>2</math> is the only [[prime]] even integer.
  
 
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Revision as of 16:54, 28 October 2013

An even integer is any integer which is a multiple of $2.$ The even integers are $\ldots, -4, -2, 0, 2, 4, \ldots$; specifically, note that $0$ is even. Every even integer can be written in the form $2k$ for some unique integer $k$.

The sum and difference of any two even integers is even, and the product of any two even integers is not only even but is also divisible by $4.$ The sum of an even integer and an odd integer is odd.

Since every even integer is divisible by $2,$ $2$ is the only prime even integer.

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