[Tex/LaTex] How to change numbering in remark

Question

I am writing a book on mathematics. I want to get the following text document :

I have written the following code :

\documentclass{book}
\usepackage{amsthm}
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\theoremstyle{definition}
\newtheorem*{example}{Example}
\newtheorem{definition}{Definition}
%\theoremstyle{remark}
\newtheorem{remark}{Remark}


\begin{document}    

\chapter{Number Theory}
\section{Congruence}
\begin{theorem}
Here is my theorem.
\end{theorem}
\begin{remark}
 Text
\end{remark}


\begin{remark}
 Text
\end{remark}


\begin{remark}
 Text
\end{remark}
\begin{proposition}
 Here is my proposition.
\end{proposition}
\begin{remark}
 Text
\end{remark}


\begin{remark}
 Text
\end{remark}
\begin{lemma}
 Here is my lemma.
\end{lemma}
\begin{remark}
 Text
\end{remark}

\end{document}  

This produces :

But I don't like this style. How can I change "remark" number ? Also I want the font in proposition "normal font".

Answer 1

Here is some code that addresses your concerns (but please rethink if you want to confuse your readers! Please!):

\documentclass{book}
\usepackage{amsthm}
\newtheoremstyle{myplain}% name
{3pt}% Space above
{3pt}% Space below
{\itshape}% Body font
{}% Indent amount
{\bfseries}% Theorem head font
{}% Punctuation after theorem head
{.5em}% Space after theorem head
{}% Theorem head spec (can be left empty, meaning `normal')

\newtheoremstyle{mypro}% name
{3pt}% Space above
{3pt}% Space below
{}% Body font
{}% Indent amount
{\bfseries}% Theorem head font
{}% Punctuation after theorem head
{.5em}% Space after theorem head
{}% Theorem head spec (can be left empty, meaning `normal')

\theoremstyle{myplain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}

\theoremstyle{mypro}
\newtheorem{proposition}{Proposition}[section]
\newtheorem{remark}{Remark}[proposition]
\newtheorem*{remark*}{Remark} %For having unnumbered remarks.  

\theoremstyle{definition}
\newtheorem*{example}{Example}
\newtheorem{definition}{Definition}

\renewcommand{\theremark}{\arabic{remark}}

\begin{document}    

\chapter{Number Theory}
\section{Linear Congruences}
\begin{theorem}
Here is my theorem.
\end{theorem}
\begin{remark}
 Text
\end{remark}


\begin{remark}
 Text
\end{remark}


\begin{remark}
 Text
\end{remark}
\begin{proposition}
 Here is my proposition.
\end{proposition}
\begin{remark}
 Text
\end{remark}


\begin{remark}
 Text
\end{remark}
\begin{lemma}
 Here is my lemma.
\end{lemma}
\begin{remark*}
 Text
\end{remark*}

\end{document}

The annotations for the theoremstyle are taken verbatim from the AMS guide to amsthm (available here).