System of equations
Source: Czech and Slovak Olympiad 2019, National Round, Problem 1
June 6, 2019
algebranational olympiadsystem of equations
Problem Statement
Find all triplets such that
\begin{align*}
x^2-yz &= |y-z|+1, \\
y^2-zx &= |z-x|+1, \\
z^2-xy &= |x-y|+1.
\end{align*}