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Number of Real Solutions of The System of The Equations

Source: LXII Polish Olympiad 2011, Problem 3

May 24, 2011
algebra unsolvedalgebra

Problem Statement

Let n≥3n\geq 3 be an odd integer. Determine how many real solutions there are to the set of nn equations {x1(x1+1)=x2(x2−1)x2(x2+1)=x3(x3−1)⋮xn(xn+1)=x1(x1−1)\left\{\begin{array}{cc}x_1(x_1+1)=x_2(x_2-1)\\x_2(x_2+1)=x_3(x_3-1)\\ \vdots \\ x_n(x_n+1) = x_1(x_1-1)\end{array}\right.
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