RO-TST 1990 Problem 7

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 $[x_n^2]=n$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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