Problem

Source: Czech and Slovak Olympiad 2019, National Round, Problem 1

Tags: algebra, national olympiad, system of equations



Find all triplets $(x,y,z)\in\mathbb{R}^3$ such that \begin{align*} x^2-yz &= |y-z|+1, \\ y^2-zx &= |z-x|+1, \\ z^2-xy &= |x-y|+1. \end{align*}