NMC 2006 Problem 2

The real numbers $x, y$ and $z$ are not all equal and satisfy

$x+\frac{1}{y}=y+\frac{1}{z}=z+\frac{1}{x}=k$

Determine all possible values of $k$ .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

k = \pm 1

Solutions

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