The sequence $\{x_n\}_n$ is defined as follows: $x_1 = 0$, and for all $n \ge 1$ $$(n + 1)^3 x_{n+1} = 2n^2 (2n + 1)x_n + 2(3n + 1).$$Prove that $\{x_n\}_n$ contains infinitely many integer numbers.
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Tags: number theory, 4th edition
The sequence $\{x_n\}_n$ is defined as follows: $x_1 = 0$, and for all $n \ge 1$ $$(n + 1)^3 x_{n+1} = 2n^2 (2n + 1)x_n + 2(3n + 1).$$Prove that $\{x_n\}_n$ contains infinitely many integer numbers.