Vol. 8, No. 2, 2019

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On a theorem of Hildebrand

Carsten Dietzel

Vol. 8 (2019), No. 2, 189–191

We give a short proof that for each multiplicative subgroup H of finite index in + , the set of integers a with a,a + 1 H is an IP-set. This generalizes a theorem of Hildebrand concerning completely multiplicative functions taking values in the k-th roots of unity.

IP-set, multiplicative subgroup
Mathematical Subject Classification 2010
Primary: 11B75
Received: 29 January 2019
Revised: 7 February 2019
Accepted: 22 February 2019
Published: 20 May 2019
Carsten Dietzel
Institute of algebra and number theory
University of Stuttgart