Problem

Source: Romania TST 1990

Tags: function, induction, algebra unsolved, algebra



The sequence $ (x_n)_{n \geq 1}$ is defined by: $ x_1=1$ $ x_{n+1}=\frac{x_n}{n}+\frac{n}{x_n}$ Prove that $ (x_n)$ increases and $ [x_n^2]=n$.