composite number
CompositeNumber
2002-05-23 00:16:16
2004-09-10 10:27:42
Definition
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A \emph{composite number} is a positive integer which is not prime and not equal to 1. That is, $n$ is composite if $n = ab$, with $a$ and $b$ natural numbers both not equal to 1.
\paragraph{Examples.}
\begin{itemize}
\item 1 is not composite (and also not prime), by definition.
\item 2 is not composite, as it is prime.
\item 15 is composite, since $15 = 3\cdot 5$.
\item 93555 is composite, since $93555 = 3^5\cdot 5 \cdot 7 \cdot 11$.
\item 52223 is not composite, since it is prime.
\end{itemize}
More generally, we can define compositeness any time there is an ambient notion of an irreducible element. In an integral domain, for example, an element is said to be \emph{composite} if it neither zero, a unit, nor irreducible.