%%% This file is part of PlanetMath snapshot of 2009-01-12
%%% Primary Title: divisibility
%%% Primary Category Code: 11A51
%%% Filename: Divisibility.tex
%%% Version: 7
%%% Owner: mathcam
%%% Author(s): mathcam, vampyr
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\begin{document}

 Given \htmladdnormallink{integers}{http://planetmath.org/encyclopedia/RationalInteger.html} $a$ 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 \htmladdnormallink{divisible}{http://planetmath.org/encyclopedia/DivisibilityOfIdeals.html} 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 \htmladdnormallink{rings}{http://planetmath.org/encyclopedia/UnitalRing.html} (e.g., \htmladdnormallink{polynomials}{http://planetmath.org/encyclopedia/Monomial2.html}).

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