MathDB

x_1^{x_2}=x_2^{x_3}=...=x_{n-1}^{x_n}=x_n^{x_1} solve in Q+

Source: Balkan MO Shortlist 2013 N9 BMO

March 10, 2020

number theoryrational

Problem Statement

Let

n\ge 2

be a given integer. Determine all sequences

x_1,...,x_n

of positive rational numbers such that

x_1^{x_2}=x_2^{x_3}=...=x_{n-1}^{x_n}=x_n^{x_1}