English

Hilbert cubes in arithmetic sets

Number Theory 2015-10-20 v1 Combinatorics

Abstract

We show upper bounds on the maximal dimension dd of Hilbert cubes H=a0+{0,a1}++{0,ad}S[1,N]H=a_0+\{0,a_1\}+\cdots + \{0, a_d\}\subset S \cap [1, N] in several sets SS of arithmetic interest such as the squares, powerful numbers and pure powers.

Keywords

Cite

@article{arxiv.1510.05260,
  title  = {Hilbert cubes in arithmetic sets},
  author = {Rainer Dietmann and Christian Elsholtz},
  journal= {arXiv preprint arXiv:1510.05260},
  year   = {2015}
}

Comments

19 pages; to appear in Revista Matem\'atica Iberoamericana; this paper supersedes the earlier preprint arXiv:1207.1461

R2 v1 2026-06-22T11:23:06.592Z