Difference between revisions of "Odd integer"

 
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An '''odd integer''' <math>n</math> is an [[integer]] which is not a [[multiple]] of 2.  Every odd integer can be written in the form <math>2k + 1</math> for some unique other integer <math>k</math>. The odd integers with smallest [[absolute value]] are <math>1, -1, 3, -3, 5, -5, \ldots</math>.  The product of any two odd integers is odd, but the sum and difference of any two odd integers are [[even integer | even]].
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An '''odd integer''' <math>n</math> is an [[integer]] which is not a [[multiple]] of <math>2</math> (or equivalently one more than a multiple of <math>2</math>). The odd integers are <math>\ldots, -5, -3, -1, 1, 3, 5, \ldots.</math>  Every odd integer can be written in the form <math>2k + 1</math> for some unique other integer <math>k</math>.   
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The product of any two odd integers is odd, but the sum and difference of any two odd integers are [[even integer | even]].
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The sum and difference of an [[even integer]] and odd integer are odd. Besides <math>2,</math> all [[prime number | prime numbers]] are odd.
  
  
 
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Revision as of 17:58, 28 October 2013

An odd integer $n$ is an integer which is not a multiple of $2$ (or equivalently one more than a multiple of $2$). The odd integers are $\ldots, -5, -3, -1, 1, 3, 5, \ldots.$ Every odd integer can be written in the form $2k + 1$ for some unique other integer $k$.

The product of any two odd integers is odd, but the sum and difference of any two odd integers are even.

The sum and difference of an even integer and odd integer are odd. Besides $2,$ all prime numbers are odd.


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