🚀 go-pugleaf

Here is the JLaTeX text of the Japanese Version of 34th IMO problems.
Requires Japanese Version of TeX by Sakurai and Isozaki (so called NTT
JTeX) to compile. Please enjoy it.

This is the text which I made after the contest. In the contest photo
copies of hand written problems are used.

Naomasa MARUYAMA (Deputy leader of IMO34 Japan Team)

$@E}?t8&$N4];3$G$9!#Bh#3#42s9q:]?t3X%*%j%s%T%C%/$NLdBj$G$9!#(JNTT JLaTeX
$@$N(J text $@$G$9!#(J

$@$3$l$OBg2q=*N;8e$K;d$,(J JLaTeX $@$KD>$7$?$b$N$G!"K\HV$G$O<j=q$-$NLdBj$r%3(J
$@%T!<$7$?$b$N$,F|K\$NA*(J$@<j$KG[$i$l$^$7$?!#(J

% style for NTT jLATEX
\documentstyle[12pt]{jarticle}

% style for ASCII jLATEX
%\documentstyle[11pt,a4j]{jarticle}

\renewcommand{\thefootnote}{\fnsymbol{footnote}}

\title{$@Bh#3#42s(J$@9q:]?t3X%*%j%s%T%C%/(J\footnotemark \\
       $@#1#9#9#3G/!"%$%9%?%s%V!<%k(J}
\footnotetext{Original copyright \copyright 1993 by IMO93 Problem Committee}
\footnotetext{This {\lower.5ex\hbox{\rm J}\kern-.1em\LaTeX} version
  is made by Mathematical Olympiad Foundation of Japan}
\footnotetext{Copyright \copyright 1993 by Mathematical Olympiad
  Foundation of Japan}
\footnotetext{$@Cx:n8"$O?t3X%*%j%s%T%C%/:bCD$K(J$@5"B0$7$^$9(J.}
\date{}
\author{}
\pagestyle{empty}
\begin{document}
\maketitle\thispagestyle{empty}
\newcommand{\IND}{\hspace*{2em}}

Version: {\bf Japanese} \hfill 1993$@G/(J7$@7n(J18$@F|(J \\

\begin{Large}
\begin{center}
$@Bh#1F|L\(J
\end{center}
\end{Large}

\begin{itemize}
\item[1.] $f(x)=x^n+5x^{n-1}+3$ $@$H$*$-!"(J $n$$@$O(J1$@$h$jBg$-$J@0?t$H(J
      $@$9$k!#$3$N$H$-(J $f(x)$ $@$r(J1$@<!0J>e$N@0?t78?tB?9`<0$U$?$D$N@Q$KJ,2r(J
      $@$9$k(J$@$3$H$OIT2DG=$G$"$k$3$H$r>ZL@$;$h!#(J

\item[2.] $@E@(JD$@$O1T3Q;03Q7A(JABC$@Fb$NE@$G(J
      \begin{description}
        \item \IND ${\rm \angle{ADB} = \angle{ACB} + 90^\circ }$
        \item \IND ${\rm AC \cdot BD = AD \cdot BC }$
      \end{description}
      $@$r$_$?$9$b$N$H$9$k!#(J
      \begin{description}
        \item[(a)] ${\rm \frac{AB \cdot CD}{AC \cdot BD} }$ $@$NCM$r5a$a$h!#(J
        \item[(b)] ${\rm \triangle{ACD} }$, ${\rm \triangle{BCD} }$
          $@$N30@\1_$NE@(JC$@$K$*$1$k@\@~$OD>8r$9$k$3$H$r>ZL@$;$h!#(J
      \end{description}

\item[3.] $@L58B$K9-$$%A%'%9HW>e$G<!$NM7$S$r$9$k!#(J    \\
      $@3+;O;~$K$O(J $n^2$ $@8D$N(J$@6p$,(J $n \times n$ $@$N@5J}7A>u$KJB$Y$i$l$F(J
      $@$$$k!#$R$H$D$N%^%9$K$O$R$H$D$N6p$7$+CV$1$J$$!#$3$N%2!<(J$@%`$G5v$5$l$k(J
      $@F0$-$O!"=DNY$j$^$?$O2#NY$j$K6p$,$"$k$H$-$=$l$r$R$H$DHt$S1[$7$F$U$?$D(J
      $@$H$J$j$N(J$@6u$$$?%^%9$K0\F0$9$k$3$H$N$_$G$"$k!#$3$N$H$-Ht$S1[$5$l$?6p$O(J
      $@HW>e$+$i<h$j=|$+$l$k!#(J \\
      $@$=(J$@$l$G$OHW>e$K6p$r$R$H$D$@$1;D$7$F%2!<%`$r=*$($k$3$H$,$G$-$k$h$&$J(J $n$
      $@$r7hDj$;$h!#(J

\end{itemize}

\begin{flushleft}
$@G[E@3F(J7$@E@(J \\
$@2rEz;~4V(J 4$@;~4V(J30$@J,(J
\end{flushleft}

\newpage

Version: {\bf Japanese} \hfill 1993$@G/(J7$@7n(J19$@F|(J \\

\begin{Large}
\begin{center}
$@Bh#2F|L\(J
\end{center}
\end{Large}

\begin{itemize}

\item[4.] $@J?LL>e$N;0E@(JP,Q,R$@$KBP$7;03Q7A(JPQR$@$N;0$D$N9b$5$N$&$A:G>.$NCM$r(J
      $m({\rm PQR})$ $@$H(J$@=q$/!#!J$?$@$7(JP,Q,R$@$,0lD>@~>e$K$"$k$H$-$O(J
      $m({\rm PQR})=0$ $@$H$9$k!#!K(JA,B,C$@$rJ?LL>e$NM?$($i$l$?E@(J$@$H$9$k!#(J
      X$@$rJ?LL>e$NG$0U$NE@$H$9$k$H$-<!$r>ZL@$;$h!#(J
      \begin{description}
        \item \IND $m({\rm ABC}) \leq m({\rm ABX}) + m({\rm AXC}) + m({\rm XBC})$
      \end{description}

\item[5.] ${\bf N}=\{1,2,3,\cdots\}$ $@$H$9$k!#(J \\
      $@4X?t(J$f: {\bf N}\rightarrow {\bf N}$ $@$G0J2<$N>r7o$r$_$?$9(J$@$b$N$,B8:_(J
      $@$9$k$+H]$+7hDj$;$h!#(J
       \begin{tabbing}
        \IND \= \hspace*{5cm} \= \kill
        \> $f(1)=2$ \\
        \> $f(f(n))=f(n)+n$ \> $n \in {\bf N}$ $@$OG$0U(J \\
        \> $f(n) < f(n+1)$  \> $n \in {\bf N}$ $@$OG$0U(J \\
       \end{tabbing}

\item[6.] $n$$@$O(J1$@$h$jBg$-$J@0?t$H$9$k!#(J$n$$@8D$N(J$@%i%s%W(J$L_0,L_1,\cdots,L_{n-1}$
      $@$,1_<~>e$KJB$s$G$$$k!#3F%i%s%W$O(JON$@$^$O$?(JOFF$@$N$$$:$l$+$N>uBV$r$H$l(J$@$k!#(J
      $@0lO"$NA`:n(J$S_0,S_1,\cdots,S_i,\cdots$$@$r9T$J$&!#A`:n(J$S_j$$@$O%i%s%W(J
      $L_j$$@$N>uBV$N$_(J
      $@$K1F6A$r5Z$\$9!JB>$N%i%s%W$N>uBV$rJQ$($J$$!K<!$N$h$&$J$b$N$G$"$k!#(J
      \begin{description}
        \item $@$b$7(J$L_{j-1}$$@$,(JON$@$J$i$P(J$S_j$$@$K$h$j(J$L_j$$@$N(JON,OFF$@$N>uBV$OH?E>$9$k!#(J
        \item $@$b$7(J$L_{j-1}$$@$,(JOFF$@$J$i$P(J$S_j$$@$K$h$j(J$L_j$$@$N>uBV$OJQ$o$i$J$$!#(J
      \end{description}
      $@%i%s%W$K$O(Jmodulo n$@$GHV(J$@9f$,$D$1$i$l$F$$$k!#$9$J$o$A(J
      \begin{description}
        \item $L_{-1}=L_{n-1},L_0=L_n,L_1=L_{n+1},\cdots$
      \end{description}
      $@:G=i$9$Y$F$N%i%s%W$O(JON$@$G$"$k!#$3$N$H$-0J2<$N$3$H$r>ZL@$;$h!#(J
      \begin{itemize}
      \item[(a)] $@$"$k@5@0?t(J$M(n)$$@$,B8:_$7!"(J$M(n)$$@2sL\$NA`:n$ND>8e$K$9$Y$F$N(J
            $@%i%s%W$,(JON$@$K$J$k!#(J
      \item[(b)] $n$$@$,(J$2^k$$@$N7A$J$i$P!"(J$n^2-1$$@2sL\$NA`:n$ND>8e$K$9$Y$F$N(J
            $@%i%s%W$,(JON$@$K$J$k!#(J
      \item[(c)] $n$$@$,(J$2^k+1$$@$N7A$J$i$P!"(J$n^2-n+1$$@2sL\$NA`:n$ND>8e$K$9(J$@$Y$F$N(J
            $@%i%s%W$,(JON$@$K$J$k!#(J
      \end{itemize}
\end{itemize}

\begin{flushleft}
$@G[E@3F(J7$@E@(J \\
$@2rEz;~4V(J 4$@;~4V(J30$@J,(J
\end{flushleft}

\end{document}

--
1993$@G/(J08$@7n(J12$@F|(J($@LZ(J)
--------
$@4];3D>>;!wE}7W?t(J$@M}8&5f=j(J
maruyama@ism.ac.jp