MathDB
Cyclic equations

Source: IMC 2012, Day 2, Problem 4

July 29, 2012
functionlinear algebramatrixalgebrapolynomialtrigonometryfloor function

Problem Statement

Let n≥2n \ge 2 be an integer. Find all real numbers aa such that there exist real numbers x1,x2,…,xnx_1,x_2,\dots,x_n satisfying x1(1−x2)=x2(1−x3)=⋯=xn(1−x1)=a.x_1(1-x_2)=x_2(1-x_3)=\dots=x_n(1-x_1)=a.
Proposed by Walther Janous and Gerhard Kirchner, Innsbruck.
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