Erdős Problem #1149

Let $\alpha>0$ be a real number, not an integer. The density of integers $n\geq 1$ for which $(n,\lfloor n^\alpha\rfloor)=1$ is $6/\pi^2$.

#1149: [Va99,1.34]

number theory

This is true, and was proved by Bergelson and Richter [BeRi17].

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This page was last edited 23 January 2026.

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