Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2503.22700 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918136559697920 |
|---|---|
| author | Ding, Yuchen |
| author_facet | Ding, Yuchen |
| contents | Let $\mathbb{N}$ and $\mathcal{P}$ be the sets of natural numbers and primes, respectively. Motived by an old problem of Erd\H os and Kalmár, we prove that for almost all $y>1$ the lower asymptotic density of integers of the form $p+\lfloor y^k\rfloor~(p\in \mathcal{P},k\in \mathbb{N})$ is positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Romanoff type problem of Erdős and Kalmár Ding, Yuchen Number Theory Let $\mathbb{N}$ and $\mathcal{P}$ be the sets of natural numbers and primes, respectively. Motived by an old problem of Erd\H os and Kalmár, we prove that for almost all $y>1$ the lower asymptotic density of integers of the form $p+\lfloor y^k\rfloor~(p\in \mathcal{P},k\in \mathbb{N})$ is positive. |
| title | On a Romanoff type problem of Erdős and Kalmár |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.22700 |