Let x, y, and z be nonzero real numbers, such that no two are equal, and
\(x + \frac{1}{y} = y + \frac{1}{z} = z + \frac{1}{x}. \)
Find all possible numeric values of xyz.
You can isolate x, y, z to get that the possible values of xyz are -2, -1, 1, and 2.
