Aflati toate functiile injective

[Claudiu Mindrila]

Fie \( \left\{ x_{1},\ x_{2},\ldots,\ x_{n}\right\} \subset\mathbb{R},\ n\in\mathbb{N},\ n\ge3 \), impar. Sa se determine toate functiile injective \( f:\left\{ x_{1},\ x_{2},\ldots,\ x_{n}\right\} \to\left\{ x_{1},\ x_{2},\ldots,\ x_{n}\right\} \) care au proprietatea: \( \left|f\left(x_{1}\right)-x_{1}\right|=\left|f\left(x_{2}\right)-x_{2}\right|=\ldots=\left|f\left(x_{n}\right)-x_{n}\right| \).

Romeo Ilie, ONM 1992