MathDB

Let

n>1

be an integer. Find all

r\in \mathbb{R}

so that the system of equations in real variables

x_1, x_2, \dots, x_n

: \begin{align*} &(r\cdot x_1-x_2)(r\cdot x_1-x_3)\dots (r\cdot x_1-x_n)=\\ =&(r\cdot x_2-x_1)(r\cdot x_2-x_3)\dots (r\cdot x_2-x_n)=\\ &\qquad \qquad \qquad \qquad \vdots \\ =&(r\cdot x_n-x_1)(r\cdot x_n-x_2)\dots (r\cdot x_n-x_{n-1}) \end{align*} has a solution where the numbers

x_1, x_2, \dots, x_n

are pairwise distinct.

Problem Statement