Difference between revisions of "Odd integer"

m
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
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>.   
+
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 integer <math>k</math>.   
  
The product of any two odd integers is odd, but the sum and difference of any two odd integers are [[even integer | even]].
+
The product of any two odd integers is odd and the result of a division where both the dividend and the divisor are odd is odd. But the sum and difference of any two odd integers are [[even integer | even]].
  
 
The sum and difference of an [[even integer]] and odd integer are odd. Besides <math>2,</math> all [[prime number | prime numbers]] are odd.
 
The sum and difference of an [[even integer]] and odd integer are odd. Besides <math>2,</math> all [[prime number | prime numbers]] are odd.
 
+
Also, odd integers are really cool
  
 
{{stub}}
 
{{stub}}

Latest revision as of 15:11, 29 March 2020

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 integer $k$.

The product of any two odd integers is odd and the result of a division where both the dividend and the divisor are odd 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. Also, odd integers are really cool

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS