MutuallyCoprime 2004-04-14 02:49:09 2004-04-14 05:39:04 Definition coprime pairwise coprime % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Natural numbers $a_1,a_2,\dots,a_n$ are called \emph{mutually coprime} if there is no $p\in\mathbb{N}$, $p>1$ with $p|a_i$ for all $i\leq n$. By this definition for example $15$, $21$ and $25$ would be mutually coprime though they are not \emph{pairwise coprime}, because that would \PMlinkescapetext{mean} that each pair of these numbers is coprime.