Find all solutions to the system
Source: Turkey IMO TST 1995 #1
July 8, 2011
algebrapolynomialalgebra unsolved
Problem Statement
Given real numbers , find all solutions of the system
\begin{align*}
&x_1^2+2ax_1+b^2=x_2,\\
&x_2^2+2ax_2+b^2=x_3,\\
&\qquad\cdots\cdots\cdots\\
&x_n^2+2ax_n+b^2=x_1.
\end{align*}