Problem

Source: Turkey IMO TST 1995 #1

Tags: algebra, polynomial, algebra unsolved



Given real numbers $b \geq a>0$, 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*}