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divisibility
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(Definition)
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Given integers $a$ and $b$ then we say $a$ divides $b$ if and only if there is some $q \in \mathbb{Z}$ such that $b=qa$
There are many other ways in common use to express this relationship:
- $a\mid b$ (read ``$a$ divides $b$ ').
- $b$ is divisible by $a$
- $a$ is a factor of $b$
- $a$ is a divisor of $b$
- $b$ is a multiple of $a$
The notion of divisibility can apply to other rings (e.g., polynomials).
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"divisibility" is owned by mathcam. [ full author list (2) | owner history (1) ]
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See Also: least common multiple, example of gcd,  function, exactly divides, divisor sum of an arithmetic function, strict divisibility, fundamental theorem of arithmetic, number theory
| Other names: |
divides, divisor, factor, multiple |
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Cross-references: polynomials, rings, divisible, integers
There are 406 references to this entry.
This is version 7 of divisibility, born on 2001-11-16, modified 2007-09-11.
Object id is 923, canonical name is Divisibility.
Accessed 25650 times total.
Classification:
| AMS MSC: | 11A51 (Number theory :: Elementary number theory :: Factorization; primality) |
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Pending Errata and Addenda
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