$(x_n)$ be a sequence with $x_1=0$, $$x_{n+1}=5x_n + \sqrt{24x_n^2+1}$$. Prove that for $k \geq 2$ $x_k$ is a natural number.
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Tags: equation, Sequence, Sequences, number theory
$(x_n)$ be a sequence with $x_1=0$, $$x_{n+1}=5x_n + \sqrt{24x_n^2+1}$$. Prove that for $k \geq 2$ $x_k$ is a natural number.