English

On a problem of Romanoff type

Number Theory 2022-04-25 v3

Abstract

Let P\mathcal{P} and N\mathbb{N} be the sets of all primes and natural numbers, respectively. In this article, it is proved that there has a positive lower density of the natural numbers which can be represented by the form p+2m12+2m22,pP,m1,m2N.p+2^{m_1^2}+2^{m_2^2},p\in \mathcal{P},m_1,m_2\in \mathbb{N}. This solves a problem of Chen and Yang in 2014.

Keywords

Cite

@article{arxiv.2201.12783,
  title  = {On a problem of Romanoff type},
  author = {Yuchen Ding},
  journal= {arXiv preprint arXiv:2201.12783},
  year   = {2022}
}
R2 v1 2026-06-24T09:09:25.948Z