Difference between revisions of "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>. | 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>. | ||
| − | The sum and difference of any two | + | The sum and difference of any two integers with the same [[parity]] is even. |
| + | 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. | ||
Since every even integer is divisible by <math>2,</math> <math>2</math> is the only [[prime]] even integer. | Since every even integer is divisible by <math>2,</math> <math>2</math> is the only [[prime]] even integer. | ||
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| + | The number of even integers are in the interval <math>(0, x)</math> is equal to <math>\left\lfloor\frac {|x|}{2}\right\rfloor+1</math> | ||
{{stub}} | {{stub}} | ||
Latest revision as of 15:45, 17 January 2023
An even integer is any integer which is a multiple of 
The even integers are 
; specifically, note that 
is even. Every even integer can be written in the form 
for some unique integer 
.
The sum and difference of any two integers with the same parity is even.
The product of any two even integers is not only even but is also divisible by 
The sum of an even integer and an odd integer is odd.
Since every even integer is divisible by 
is the only prime even integer.
The number of even integers are in the interval 
is equal to 
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