Definition:Composite Number
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Definition
A composite number $c$ is a positive integer that has more than two positive divisors.
As Euclid defined it:
(The Elements: Book VII: Definition $13$)
Extension to All Integers
The definition of a composite number can be extended to all of the integers, as follows:
- A positive integer $n$ is composite iff $n$ has more than two positive divisors.
- A negative integer $n$ is composite iff $\left|{n}\right|$ is composite.
$0$ is not considered composite.
Comment
$1$ is a special case - it is neither prime nor composite. All of the other positive integers are either prime or composite.
Sources
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 12$
