English

On sequences of positive integers having no $p$ terms in arithmetic progression

Number Theory 2007-05-23 v1

Abstract

We use topological ideas to show that, assuming the conjecture of Erd\"(o)s on subsets of positive integers having no pp terms in arithmetic progression (A. P.), there must exist a subset MpM_p of positive integers with no pp terms in A. P. with the property that among all such subsets, MpM_p maximizes the sum of the reciprocals of its elements.

Keywords

Cite

@article{arxiv.math/0703467,
  title  = {On sequences of positive integers having no $p$ terms in arithmetic progression},
  author = {Goutam Pal},
  journal= {arXiv preprint arXiv:math/0703467},
  year   = {2007}
}
R2 v1 2026-07-22T17:52:44.276Z