LucasLhemer 2004-06-11 07:55:04 2008-03-08 20:01:51 Theorem % 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 \textbf{Theorem:} Let $p>2$ be a prime, and let $M_p$ be a Mersenne number, then $M_p$ is prime iff $M_p$ divides $s_{p-1}$ where the numbers $(s_n)_{n\geq1}$ are given by the following recurrence relation: $s_1=4$, and $$s_{n+1}={s_n}^2-2$$ for $n\geq1$.