divisibilityDivisibility2001-11-16 20:54:462007-09-11 13:42:55Definition\usepackage{amssymb}
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\usepackage{xypic}Given integers $a$ and $b$, then we say $a$ \emph{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:
\begin{itemize}
\item $a\mid b$ (read ``$a$ divides $b$'').
\item $b$ is divisible by $a$.
\item $a$ is a factor of $b$.
\item $a$ is a divisor of $b$.
\item $b$ is a \emph{multiple} of $a$.
\end{itemize}
The notion of divisibility can apply to other rings (e.g., polynomials).