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 <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 | + | 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 | + | 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. | ||
Revision as of 19:12, 12 February 2020
An odd integer 
is an integer which is not a multiple of 
(or equivalently one more than a multiple of ). The odd integers are 
Every odd integer can be written in the form 
for some unique integer 
.
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 
all prime numbers are odd.
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