\documentclass[11pt]{scrartcl}
\usepackage{evan}

\begin{document}
\title{Germany 2017/5}
\subtitle{Evan Chen}
\author{Twitch Solves ISL}
\date{Episode 68}
\maketitle

\section*{Problem}
Prove that for all non-negative numbers $x$, $y$, $z$ satisfying $x+y+z=1$,
one has
\[ 1 \le \frac{x}{1-yz}+\frac{y}{1-zx}+\frac{z}{1-xy}
  \le \frac{9}{8}. \]

\section*{Video}
\href{https://www.youtube.com/watch?v=hJ_r74sfBaE&list=PLi6h8GM1FA6yHh4gDk_ZYezmncU1EJUmZ}{\texttt{https://youtu.be/hJ\_r74sfBaE}}

\section*{External Link}
\url{https://aops.com/community/p8209248}

\newpage

\section*{Solution}
Subtracting $x+y+z$ shows the inequality is equivalent to
\[ 0 \le \sum_{\text{cyc}} \frac{xyz}{1-yz} \le \frac18. \]
The left-hand side is now clear since $\max(yz,zx,xy) < 1$,
and equality holds if $xyz = 0$.

I think my proof of the right-hand side is currently broken; needs fix.

\end{document}
