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Definition Suppose $k$ is an integer. If there exists an integer $r$ such that $k=2r+1$ then $k$ is an odd number. If there exists an integer $r$ such that $k=2r$ then $k$ is an even number.
The concept of even and odd numbers are most easily understood in the binary base. Then the above definition simply states that even numbers end with a $0$ and odd numbers end with a $1$
- Every integer is either even or odd. This can be proven using induction, or using the fundamental theorem of arithmetic.
- An integer $k$ is even (odd) if and only if $k^2$ is even (odd).
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"even number" is owned by mathcam. [ full author list (2) | owner history (2) ]
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See Also: odd number
| Also defines: |
odd number, even integer, odd integer, even, odd |
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Cross-references: fundamental theorem of arithmetic, induction, base, binary, integer
There are 696 references to this entry.
This is version 7 of even number, born on 2003-09-05, modified 2006-08-10.
Object id is 4703, canonical name is EvenNumber.
Accessed 37809 times total.
Classification:
| AMS MSC: | 03-00 (Mathematical logic and foundations :: General reference works ) | | | 11-00 (Number theory :: General reference works ) |
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Pending Errata and Addenda
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