MathDB

System of equations

Source: 2001 Austrian-Polish, problem 2

September 19, 2006

limitalgebrasystem of equationspigeonhole principlealgebra proposed

Problem Statement

Let

n

be a positive integer greater than

2

. Solve in nonnegative real numbers the following system of equations x_{k}+x_{k+1}=x_{k+2}^{2} , k=1,2,\cdots,n where

x_{n+1}=x_{1}

and

x_{n+2}=x_{2}