Cyclic System of Equations
Source: 2023 Polish Junior Math Olympiad Finals
May 5, 2023
number theory
Problem Statement
Determine whether there exist real numbers , , , such that x+\frac{1}{y}=z, y+\frac{1}{z}=x, z+\frac{1}{x}=y.
Source: 2023 Polish Junior Math Olympiad Finals