English

A proof of Erd\H{o}s's $B+B+t$ conjecture

Dynamical Systems 2023-11-07 v2 Combinatorics Number Theory

Abstract

We show that every set AA of natural numbers with positive upper density can be shifted to contain the restricted sumset {b1+b2:b1,b2B and b1b2}\{b_1 + b_2 : b_1, b_2\in B \text{ and } b_1 \neq b_2 \} for some infinite set BAB \subset A.

Keywords

Cite

@article{arxiv.2206.12377,
  title  = {A proof of Erd\H{o}s's $B+B+t$ conjecture},
  author = {Bryna Kra and Joel Moreira and Florian K. Richter and Donald Robertson},
  journal= {arXiv preprint arXiv:2206.12377},
  year   = {2023}
}

Comments

14 pages. Changes after referee comments, improved exposition