System of equations: max(x_i, i)=x_{i+1}
Source: Czech-Polish-Slovak 2003 Q1
April 28, 2013
algebrasystem of equationsalgebra unsolved
Problem Statement
Given an integer , solve in real numbers the system of equations \begin{align*}
\max\{1, x_1\} &= x_2 \\
\max\{2, x_2\} &= 2x_3 \\
&\cdots \\
\max\{n, x_n\} &= nx_1. \\
\end{align*}