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%\usepackage{refcheck}
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\begin{document}
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\noindent \textbf{Notes on Number Theory and Discrete
Mathematics \newline
Print ISSN 1310--5132, Online ISSN 2367--8275 \newline
Vol. xx, 2021, No. x, xx--xx\newline
DOI: 10.7546/nntdm.2021.xx.x.xx-xx}
\vspace{8mm}
\begin{center}
{\LARGE \bf Your paper title here, centered, bold}
\vspace{8mm}
{\Large \bf First Author$^1$, Second Author$^2$ and Third Author$^3$}
\vspace{3mm}
$^1$ Department of ..., University of ... \\
Institutional address, Country \\
e-mail: \url{first.author@university.edu}
\vspace{2mm}
$^2$ Department of ..., Institute of ... \\
Institutional address, Country \\
e-mail: \url{second.author@university.edu}
\vspace{2mm}
$^3$ Department of ..., University of ... \\
Institutional address, Country \\
e-mail: \url{third.author@university.edu}
\end{center}
\vspace{10mm}
\noindent
{\bf Received:} DD Month YYYY \hfill {\bf Revised:} DD Month YYYY \hfill {\bf Accepted:} DD Month YYYY \\ \\ \noindent
{\bf Abstract:} The abstract shall provide a brief summary of the paper. There is no limit set for the number of words or symbols in the Abstract. You can add the date after ``Received:''. The dates after ``Revised:'' (optional) and ``Accepted:'' are to be added by the Editor.\\
{\bf Keywords:} Keywords, More relevant keywords. \\
{\bf 2020 Mathematics Subject Classification:} XXYZZ, AABCC.
\vspace{5mm}
\section{Introduction} \label{sec:Intr}
Body text and section titles are in sentence case, font Times New Roman, 12 pt, justified. First paragraph starts with no indentation, while all the rest paragraphs start with indentation.
The line spacing is set at 1.15. No limitation of the number of pages per paper, \cite{1,2,3}.
Further to clarify when a \LaTeX command(s) is visualized we denote this by surrounding it in a box, i.e. \fbox{\texttt{commands}}.
\section{Section title}
As already mentioned, the first paragraph starts with no indentation. You may use \textit{italic} to emphasize on certain words \fbox{\texttt{\textbackslash textit\{words\}}} or \fbox{\texttt{\textbackslash emph\{words\}}} when a \emph{specific term} is being introduced in the paper for the first time.
The second paragraph starts with indentation. Complex formulas are usually placed on a separate line, centered, using:
\begin{itemize}
\item \fbox{\texttt{\$\$} \texttt{equation content} \texttt{\$\$}},
or preferably
\fbox{\texttt{\textbackslash[} \texttt{equation content}~\texttt{\textbackslash]}} for unnumbered equations or
\item \fbox{\texttt{\textbackslash begin\{equation\}}\texttt{equation content} \texttt{\textbackslash end\{equation\}}} for numbered.
\end{itemize}
Enumerated formulas can be easily arranged, as shown on the example below:
\begin{equation}\label{eq:1}
\sum_{i=1}^n \mu_i > \sum_{i=1}^n \nu_i ,
\end{equation}
where the second paragraph continues without indentation in case that the sentence before the formula has not finished.
You may create simple one-line formulas, too, but please format them properly with ``\$'': e.g. italic for the Latin and Greek variables, normal font for digits, mathematical and punctuation symbols, etc.
For multiple-lined equations that need to be aligned with respect to a specific symbol, please use:
\begin{itemize}
\item \fbox{\parbox{0.925\textwidth}{\texttt{\textbackslash begin\{equation\}}\texttt{\textbackslash begin\{aligned\}} \texttt{equation content} \texttt{\textbackslash end\{aligned\}} \texttt{\textbackslash end\{equation\}}}} if all the expressions should have a single number
\begin{equation}\label{eq2}
\begin{aligned}
x^2+y^2=2xy\\
\Gamma(n)\binom{n}{m}=(n+1)! \binom{n}{m}\\
\zeta(s)=\sum_{n=1}^{\infty} n^{-s}
\end{aligned}
\end{equation}
Refer to the equation in the text as \eqref{eq2}.
\item \fbox{\texttt{\textbackslash begin\{align\}} \texttt{equation content} \texttt{\textbackslash end\{align\}}}, if each of the equations has to be numbered separately and has to be aligned by a certain symbol. Use the command \fbox{\texttt{\textbackslash allowdisplaybreaks}} before the environment to allow the formulas to automatically break between pages. See the example below:
\allowdisplaybreaks
\begin{align}
x+y&=z \label{eq3}\\
x-y&=q \label{eq4}\\
b^2&=\Delta(x) \label{eq5}\\
u_{xx}+u_{yy}&=0 \label{eq6}
\end{align}
One can call the references in the text as usual \eqref{eq3} and \eqref{eq4}.
\item \fbox{ \texttt{\textbackslash begin\{align*\}} \texttt{equation content} \texttt{\textbackslash end\{align*\}}}, if none of the equations needs to be numbered.%
\allowdisplaybreaks
\begin{align*}
f(x)&=x^2+2x+2\\
&\geq (x+1)^2\\
& \geq x^2 \\
& = \sqrt{|x|}\\
&=A
\end{align*}
\end{itemize}
\subsection{First subsection}
In this subsection, we have text and a table (see Table~\ref{tab1}). The table itself is centered with respect of page margins, with bold headers, its contents being arranged per authors' decision.
\begin{table}[!ht]
\centering
\begin{tabular}{| c | c | c |}
\hline
\rowcolor{Gray} % Header Row is colored in gray
Header 1 & Header 2 & Header 3 \\ \hline
Cell 1.1 & Cell 1.2 & Cell 1.3 \\ \hline
Cell 2.1 & Cell 2.2 & Cell 2.3 \\ \hline
Cell 3.1 & Cell 3.2 & Cell 3.3 \\ \hline
\end{tabular}
\caption[Table caption text]{Table caption}\label{tab1}
\end{table}
Tables have to be referred to within the text and placed after the first reference, preferably within the same section (subsection) of the text. The text of the table caption is placed below the table. Tables shall ideally fit into one page only, but if longer, the header row shall repeat at the top of each page. Rows shall not break across pages.
\subsection{Second subsection}
In this subsection, we have text and a figure (Figure 1). The figure shall not exceed the page margins. The figure shall have wrapping style in line with text and shall be centered.
\begin{figure}[!ht]
\centering
\setlength{\unitlength}{2mm}
\begin{picture}(30,20)
\linethickness{0.15mm}
\multiput(0,0)(5,0){3}%
{\line(0,1){10}}
\multiput(0,0)(0,5){3}%
{\line(1,0){10}}
\end{picture}
\caption{The figure caption is 12 pt, centered}\label{fig1}
\end{figure}
Figures have to be referred to within the text and placed after the first reference, preferably within the same section (subsection) of the text. For example, see Figure~\ref{fig1}. The figure captions are consequently numbered and placed below the figures.
\begin{theorem}\label{thm:theorem1} Theorems are consequently numbered. \end{theorem}
\begin{proof} The end of each proof is marked with the right aligned square. \end{proof}
\begin{corollary}\label{cor:corollary} Corollaries by default use their own counter. \end{corollary}
\begin{lemma}\label{lem:lemma1} Lemmas by default use their own counter. \end{lemma}
\begin{theorem}\label{thm:theorem2} Theorems are consequently numbered. \end{theorem}
Therefore, when citing in the text use \fbox{ \texttt{Theorem{\raise.17ex\hbox{$\scriptstyle\sim$}}\textbackslash ref\{thereom's label\}}}. The tilde sign is an unbreakable space and ensures that the referred label will be kept together with the preceding word. Please make sure to use unique labels. For example, see Theorem~\ref{thm:theorem1}.
\section*{Acknowledgements}
Optional place for funding acknowledgements and/or expression of gratitude.
\makeatletter
\renewcommand{\@biblabel}[1]{[#1]\hfill}
\makeatother
\begin{thebibliography}{99}
% Sort references alphabetically per first author's surname.
\bibitem{1} Familyname1, N1., Familyname2, N2., \& Familyname3, N3. (1970). Title of a journal publication in sentence case. \textit{Journal Name in Italic Title Case}, 1(2), 33--45.
\bibitem{2} Familyname1, N1., Familyname2, N2., \& Familyname3, N3. (1970). \textit{Journal Name in Italic Title Case}, 1(2), Article 0034567.
\bibitem{3} Familyname1, N1., \& Familyname2, N2. (2010). Title of a conference communication in sentence case. \textit{Proceedings of 11-th International Conference}, 22--24 March 2010, Town, Country, Vol. X, 33--45.
\bibitem{4} Familyname1, N1. (1990). \textit{Title of a Monograph in Italic Title Case}. Publishing House, Town.
\bibitem{5} Familyname1, N1. (2020). \textit{Title of publication}. Website.com, Available online at: \url{http://website.com/folder/page.html}.
\end{thebibliography}
\end{document}