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arXiv · 1810.01518

On a theorem of Hildebrand

Carsten Dietzel
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Abstract

We prove that for each multiplicative subgroup $A$ of finite index in $\mathbb{Q}^+$, the set of integers $a$ with $a, a+1 \in A$ is an IP-set. This generalizes a theorem of Hildebrand concerning completely multiplicative functions taking values in the $k$-th roots of unity.

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Carsten Dietzel. 2018-10-02. On a theorem of Hildebrand. https://doi.org/10.2140/moscow.2019.8.189

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