\documentclass[a4paper,french,11pt]{article}
\usepackage[francais]{babel}
\usepackage{mathtools,amssymb,amsthm}
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%\usepackage[T1]{fontenc}
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\usepackage{fourier}
\usepackage{titlesec}
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\usepackage{hyperref}
\hypersetup{ 
	colorlinks=true,
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	urlcolor=[rgb]{0.05,0,0.25}
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\titleformat{\section}{\bfseries\Large}{\thesection.}{0.5em}{}
\titleformat{\subsection}{\bfseries\large}{\hspace{.5em}\thesubsection.}{0.5em}{}
\newtheorem{theo}{Theorem}
\newtheorem*{theo*}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorem*{prop*}{Proposition}
\newtheorem{lemma}{Lemma}
\newtheorem*{lemma*}{Lemma}
\newtheorem{cor}{Corollary}
\newtheorem*{cor*}{Corollary}
\theoremstyle{definition}\newtheorem{defn}{Definition}
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\theoremstyle{remark}\newtheorem{rem}{Remark}
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\newcounter{note}
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\fancyfoot[L]{\sffamily MATh.en.JEANS 20..-20..\empty}
\fancyfoot[C]{\sffamily School of Nowhere}
\fancyfoot[R]{\sffamily Page \thepage}
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\begin{document}
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\thispagestyle{empty}
\begin{center}
\fcolorbox[gray]{0}{0.95}{%
	\begin{minipage}[c]{.975\linewidth}
		\begin{center}\sffamily
			This article is written by students. It may include omissions and imperfections,\\
			as far as possible reported by our reviewers in the editing notes.
		\end{center}
	\end{minipage}
}

\vspace{10ex}
\huge\sffamily\textbf{Un joli titre}

\vspace{3ex}
\large
Year 20..-20..

\vspace{3ex}
Toto and Titi, $4^{\rm th}$ class
\end{center}
\vspace{2ex}
{\sffamily \large
\noindent{School(s):} School of Nowhere

\vspace{.5ex}
\noindent{Teacher(s):} Marcel Dugenou

\vspace{.5ex}
\noindent{Researcher(s):} Evariste G., Across the way  University
}

%\tableofcontents  
\vspace{2ex}
\begin{itemize}\color{red}\em
	\item As far as possible, avoid using packages other than those proposed in this model.
    \item Do not reduce the margins. 
    \item Drawings and images must be legible and include a caption. Provide them in separate files, grouped together in an archive.
    \item Do not insert text or formulas in the form of images.
\end{itemize}
\section{Introduction}

\subsection{The problem}

{\em The problem must be stated in clear terms.}

\subsection{Results}
{\em If your article is a little long, state here the main results and conjectures obtained.}

\section{Some tips for writing}
Think that readers don't know anything about your problem, unlike you who have been immersed in it for several months.

What may seem obvious to you, because you've given it a lot of thought all year,
may not be obvious to the people who read your article, especially students at the same level as you.

So you need to explain everything:
\begin{itemize}
    \item define the terms and terminology used,
    \item check that the notation is consistent both within the text and between the text and the illustrations,
    \item make clear and explicit figures, if necessary accompanied by a legend.
\end{itemize}
And above all
\begin{itemize}
    \item  justify everything that is stated.
\end{itemize}
Avoid 
\begin{itemize}
    \item too many personal comments,    \item useless illustrations.
\end{itemize}
\section{{A section}}
{\color{red}{\em Put in as many sections as you like, with appropriate titles \ldots}}

\subsection{A subsection}
{\color{red}{\em The same for subsections}}

\vspace{2ex}

\emph{Examples of mathematical environments (with or without numbering).}


\begin{defn*} A definition
\end{defn*}

\begin{theo*}[Pythagoras's Theorem]
	A classic theorem you need this article
\end{theo*}

\begin{prop*}
	A first result
\end{prop*}

\begin{theo}\label{montheo}
	Main result
\end{theo}

\begin{lemma}\label{monlemme}
	An intermediate result that will be used in the proof of the theorem
\end{lemma}

\begin{proof}
	Bla, bla, bla\ldots
	
	Bla, bla, bla\ldots
\end{proof}
\begin{proof}[Preuve du théorème \ref{montheo}]
	By applying the lemma \ref{monlemme}, \ldots
	
	\ldots
	
	and the theorem is proved.
\end{proof}

\begin{cor}
	A consequence of theorem \ref{montheo}.
\end{cor}

\begin{rem*}
	Our problem is solved!
\end{rem*}


\section{Conclusion}


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