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Quadratic system

Source: Mexico National Olympiad 2011 Problem 3

June 22, 2014
quadraticsinequalitiesalgebrasystem of equationsalgebra proposed

Problem Statement

Let nn be a positive integer. Find all real solutions (a1,a2,…,an)(a_1, a_2, \dots, a_n) to the system:
a12+a1−1=a2a_1^2 + a_1 - 1 = a_2 a22+a2−1=a3 a_2^2 + a_2 - 1 = a_3 ⋮\hspace*{3.3em} \vdots an2+an−1=a1a_{n}^2 + a_n - 1 = a_1
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