Abstract We show that an additive Hilbert cube (in prime fields) of sufficiently large dimension always meets certain kinds of arithmetic sets, namely, product sets and reciprocal sets of sumsets satisfying certain technical conditions.

中文翻译：

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希尔伯特立方体满足算术集

摘要 我们证明了一个足够大维数的加性希尔伯特立方体（在素域中）总是满足某些算术集，即满足一定技术条件的和集的乘积集和倒数集。