% This file was converted to LaTeX by Writer2LaTeX ver. 0.4
% see http://www.hj-gym.dk/~hj/writer2latex for more info
\documentclass[11pt,twoside]{article}
\usepackage[ascii]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{amsthm,amsmath,amssymb,amsfonts,textcomp}
\usepackage{color}
\usepackage{calc}
\usepackage{hyperref}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper} 

\newtheorem{theorem}{Theorem}
\theoremstyle{definition} 
\newtheorem{question}{Problem}

% Check if we are compiling under latex or pdflatex, and include the
% appropriate graphics package
\ifx\pdftexversion\undefined
 \usepackage[dvips]{graphicx}
\else
 \usepackage{graphicx}
\fi


\title{Divisibility I (continues)}
\date{}
\begin{document}
\makeatother
\maketitle


\section*{Divisibility by 2, 3, 4, 5, 7,  9,  and 11.}

 \question{How can you quickly determine whether a number is divisible by 2 or by 5? More importantly, why does this work?} 
 \bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

 \question{How can you reasonably quickly determine whether a number is divisible by 4? Can we do something a bit like what we do for 2 and 5?} 
  

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

 \question{How can you quickly determine whether a number is divisible by 3? And, this is harder, why does this work? Is there a similar approach to divisibility by 9?} 
 
 \bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

 \question{How can you quickly determine whether a number is divisible by 11? } 
  \bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

 \question{Now for the hard one, how can you reasonably quickly determine whether a number is divisible by 7? (The approach is related to the approach for 11.)} 
  


  
  
\end{document}  