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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2503.22700 |
| Etiquetas: |
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- 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.